PLEASE HELP!!Determine whether the events A and B are independent.
Eight friends are drawing straws. The one who picks the short straw must cook dinner for the others.
Event A: The first person does not pick the short straw
Event B: The second person picks the short straw
A. No
B. Yes

Answer:

I'm sure its x>10

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+7>27

Subtract 7 from both sides

2x+7−7 27−7

2x>20

Divide both sides by 2

2x/2 > 20/2

= x>10

Answer:

we need a picture of the problem

Step-by-step explanation:

Yes ,induction can be used to prove the following is true for every nonnegitive integer n.

If P (n) is true, so is P (n + 1) because this argument holds true for any nonnegative integer n, it establishes the second fact required by the induction proof. As a result of the Induction Principle, the predicate P (m) is true for all nonnegative integers, m.

Mathematical induction is a technique for proving the truth of a statement, theorem, or formula for each and every natural number n. This is generalized as the 'Principle of Mathematical Induction,' which we would use to prove any mathematical statement.

For instance, 13 +23 + 33 +..... +n3 = (n(n+1) / 2)

The statement is assumed to be true for all natural number values in this case.

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Answer:

6 2/3

Step-by-step explanation:

2 1/6 + 4 3/6

6 4/6

6 2/3

Answer:

k = -4

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}4x - 8y = -3\\2x + ky = 10\end{cases}[/tex]

Rewrite the given equations so that they are in slope-intercept form.

[tex]\begin{aligned}4x-8y&=-3\\4x&=8y-3\\4x+3&=8y\\\dfrac{4x+3}{8}&=y\\y&=\dfrac{1}{2}x+\dfrac{3}{8}\end{aligned}[/tex]

[tex]\begin{aligned}2x+ky&=10\\ky&=-2x+10\\y&=\dfrac{-2x+10}{k}\\y&=-\dfrac{2}{k}x+\dfrac{10}{k}\end{aligned}[/tex]

An inconsistent system of linear equations has no solutions and therefore the lines are parallel.  

Parallel lines have the same slope:

[tex]\implies \dfrac{1}{2}=-\dfrac{2}{k}[/tex]

[tex]\implies \dfrac{1}{2}k=-2[/tex]

[tex]\implies k=-2 \cdot 2[/tex]

[tex]\implies k=-4[/tex]

Answer:

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

Equation in the standard form ax + by = c  has:

Given system:

Compare the slopes of the two lines:

We need them to be equal:

Compare the y-intercepts of the two lines:

We need to confirm they are not same:

Confirmed, so k = -4 is our solution.

A base is a negative number and an exponent is also a negative number is explained in two ways:

(a) if the negative exponent is an even number, then the result will be a positive number.

(b) if the negative exponent is an odd number, then the result will be a negative number.

The required negative exponential formula is

a⁻ᵇ = 1/aᵇ or 1/a⁻ᵇ = aᵇ

Consider two negative numbers '-x' as the base and '-n' as the exponent.

So, the given statement in mathematical form is as below:

⇔ (-x)⁻ⁿ

Then, we can evaluate them in two ways by considering 'n' to be an even and an odd number.

(a) If 'n' is an even number:

from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write

(-x)⁻ⁿ = 1/(-x)ⁿ

Since 'n' is an even number (-x)ⁿ = xⁿ

So, the result will be a positive rational or decimal number.

I.e., (-x)⁻ⁿ = 1/xⁿ

(b) If 'n' is an odd number:

from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write

(-x)⁻ⁿ = 1/(-x)ⁿ

Since 'n' is an odd number (-x)ⁿ = -xⁿ

So, the result will be a negative rational or decimal number.

I.e., (-x)⁻ⁿ = -1/xⁿ

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In the given diagram, the arc length of the given arc is 10.46.

From the question, we are to determine the length of the arc.

From the formula for calculating the length of an arc, we have that

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by arc at the center of the circle

and r is the radius of the circle

In the given diagram,

Angle subtended = π/3 = 60°

Radius, r = 10

Thus,

The length of the arc = 60/360 × 2πr

Length of the arc = 1/6 × 2×3.14×10

Length of the arc = 10.46

Hence, the length is 10.46

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WR Answer: 10.46

Step-by-step explanation:

he length of the arc = 60/360 × 2πr

Length of the arc = 1/6 × 2×3.14×10

Length of the arc = 10.46

Hence, the length is 10.46

Proving  X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e".

Given :

If I can prove that X is c.e. and ω∖X is c.e. then I can prove that X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e". But I'm not able to proceed on how should I do this.

Take a computable surjection :

f : ω → W.

Defined  G = { f ( x ) ∣ x ∈ ω and ∀y < x ( f ( y ) < f ( x ) ) }.

here clearly, G ⊆ W .

And G is infinite. For if f ( x ) ∈ G, take the smallest y such that f ( y ) > f ( x ); then f ( y ) ∈ V.

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The mathematical expression for the work performed by the spring and the cubic term is W=3.3488J C=%3.4

The spring's and the cubic term's labor Question Parameters:

How much effort is required to compress this spring 15 cm

Take into account a spring with k = 250 N/m and q = 900 N/m3.

In general, the mathematical formula for the force is given as

(FSp)s=−kΔs−q(Δs)^3

Location of Work done

W = int dxF.

Hence

W=3.3488J

b)Where a cubic term is mathematically given as

C={0.1139}/{3.3488}

C=%3.4

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As reported by the Bureau of Labor Statistics, the inflation rate of CPI for Airfare from 2263 and 22264 is - 0.06198 ( disinflation).

We have given that,

The CPI for Airfare in 2263 = 579.6

The CPI for Airfare in 2262 = 617.9

Base year is 1914 ,

Following the formula which is used to calculate inflation rate of airfare from 2263 to 2263

Inflation= (CPI₂₂₆₃ - CPI₂₂₆₂)/CPI₂₂₆₂

= (579.6 - 617.9)/617.9

= - 153.8/617.9

= - 0.06198

= 6.198%

Since , the inflation is negative this means that the economy is experiencing disinflation of 6.198%.

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So for a gallon of punch, you would need around two thirds of a cup of cranberry juice.

Equations go into one of two categories: identities or conditional equations. An identity holds true for each value of the variables. A conditional equation is valid only for certain values of the variables. An equation is represented by the equals sign ("="), which separates two expressions.

Here,

In essence, this can be set up in a proportion.

Two cups of cranberry juice are required per gallon of punch. The quantity of cranberry juice required for one gallon is what you need to determine. So, in order to set up your percentage, do as follows:

Following cross-multiplication, you should have the following:

=> 3x = 2

then division should result in this:

=> x = 2/3

So for a gallon of punch, you would need around two thirds of a cup of cranberry juice.

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Answer:

420 feet.

Step-by-step explanation:

We have to first multiply 25 times 12 (because 6 hours is 12 half hours) which is 300.
300 plus his starting point, 120 is 420.

Therefore, your answer is 420 feet.

Answer: 420 feet

Step-by-step explanation:

Because Daniel climbed 25 feet every half hour for 6 hours, 25 feet is added 12 times to the 120 feet he already climbed.

120 + (25 × 12)

25 × 12 = 300

120 + 150 = 420

Answer:

All Correct! The corinates on the graph are all graphed in the correct position.

Answer:

Yes, you are correct.

Step-by-step explanation:

(a) The point estimate of the population variance is 400

(b) According to the 90% confidence interval, the population variance is 152 ≤ σ² ≤ 800

(c) According to the 90% confidence interval, the population standard deviation is 23.8 ≤ σ ≤  41.1

Standard deviation

in probability, standard deviation refers the measure of how dispersed the data is in relation to the mean.

Given,

Here we know that because of staffing decisions, managers of the a certain hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 25 days of operation shows a sample mean of 300 rooms occupied per day and a sample standard deviation of 20 rooms.

Here we need to find the following.

a)  Here the point estimate of the population variance is calculated as,

=> Square of S = S²

The value of S is 20

=> 20² = 400

b) As per the confidence interval, the population variance is calculated as,

n = 20

S² = 400

Then the variance is

=> (n-1)s²/0.05  ≤ σ² ≤  (n-1)s²/0.95

When we apply the values on the equation, then we get

=>  (20-1) x 400/0.05  ≤ σ² ≤  (20 - 1) x 400/0.95

Variation 152 ≤ σ² ≤ 800

c) Finally, the Standard Deviation is calculated as,

=> 23.8 ≤ σ ≤  41.1

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The area of a trapezoid is 136[tex]cm^{2}[/tex].

we know that the area of a trapezoid is:

Area= 1/2 * (a+b) * h

where a and b are the lengths of the parallel sides of the trapezoid, and h is the height.

Now as per the question,

first parallel side, a = 12cm

second parallel side, b = 22cm

height, h =8cm

Area of a trapezoid = 1/2 * (12+22) *8 [tex]cm^{2}[/tex]

                                 = 136[tex]cm^{2}[/tex]

Therefore, the area of a trapezoid is 136[tex]cm^{2}[/tex].

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Using Pythagoras theorem, the length of AE in the square  2√2 unit

To find the length of side AE, we have to use use the dimension of BD given.

In the figure given, the length of all sides are equal to one another. This implies that the sides are equidistant to one another.

In a given square, all the sides are equal to one another, but the length of the diagonal is the square root of the sum of two sides

This can be further explained as

BD = AC

Using Pythagoras theorem

BD² = AD² + BA²

4² = x² + x²

16 = 2x²

x² = 8

x = √8

x = 2√2

However, we need to find the length of AE

AE is half the length size of AD

AE = 2√2 / 2

AE = √2

The distance AE = √2

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Answer:

It's 37

Step-by-step explanation:

Answer: 37

Step-by-step explanation:

[tex]\displaystyle\\20-(2)(-7)+(-9)\div(-3)=\\\\20-(-14)+\frac{-9}{-3}=\\\\20+14+3=\\\\37[/tex]

The required invested money is given as $2200.

Harriett Weiss earned $77 in simple interest in 6 months at an annual interest rate of 7%.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

Here,

Applying the standard formula for the simple interest.
SI  = principal × rate × time / 100
77 =[ p × 7 × 6/12 ]/ 100
p = 77 / 7 × 2 × 100
p = 11 × 200
p = 2200

Thus, the required investment amount is specified as $2200.

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The distributive property of 25+45 is 25+45 = 5(5+9).

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Say you wish to multiply 5 by the product of 10 plus 3.

When two terms are similar, we often sum the two amounts before multiplying by 5. 5(10 + 3) = 5(13) = 65.

So, the distributive property of 25+45:

25+45 = 5(5+9)

Therefore, the distributive property of 25+45 is 25+45 = 5(5+9).

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Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

If 60% of the population supports massive federal budget cuts.

We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.

So, the probability is, 155 / 250 = 0.62

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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The coordinate of T ' will be;

⇒ T ' = (- 31, - 23)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

This is a Dilation with a scale factor of 4 (D4).

Now,

Since, The Center of Dilation of this transformation is at the center. But the transformation is given by a scale factor of 4 and adding to (-3,1) as;

⇒ T ' = 4 (- 7, - 6) + (-3, 1)

        = (- 28, - 24) + (-3, 1)

        = (- 31, - 23)

Thus, The coordinate of T ' = (- 31, - 23)

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Rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y = [tex]\frac{5}{4}x+1[/tex].

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

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If the domain of f(x) = x² - 4 is limited to {-1, 0, 1, 2} the greatest value of the range is 0

The range represents the output values

Using the given expression to solve it can be found that the output values are

for x = -1, f(x) = x² - 4 = -1² - 4 = -3

for x = 0,  f(x) = x² - 4 = 0² - 4 = -4

for x = 1, f(x) = x² - 4 = 1² - 4 = -3

for x = 2, f(x) = x² - 4 = 2² - 4 = 0

The greatest value of the range is 0

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An algorithm is a collection of clear instructions for solving a specific issue in computer programming.

Step 1: Start

Step 2: Declare variables num1, num2 and sum.

Step 3: Read values num1 and num2.

Step 4: Add num1 and num2 and assign the result to sum.

       sum←num1+num2

Step 5: Display sum

Step 6: Stop

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If suppose all firms at industry are well merged into a single, then the Herfindahl index must become 10,000. Option (c) is correct.

A merger among organizations generating exclusive items or offerings for one particular completed product. A vertical merger takes place whilst or greater firms, working at exclusive ranges inside an industry's deliver chain, merge operations. Historically, mergers and acquisitions generally tend to end result in process losses.

Most of that is as a consequence of redundant operations and efforts to enhance efficiency. The threatened jobs encompass the goal company's CEO and different senior management, who regularly are provided a severance bundle and allow go."). Some not unusualplace synonyms of merge are amalgamate, blend, coalesce, commingle, fuse, mingle, and mix. While these kinds of phrases mean "to mix right into a greater or much less uniform whole," merge indicates a combining wherein one or greater factors are misplaced withinside the whole.

If all firms were merged at HHI, then it would be:

1. add all share market percent

2. take square of step 1

=(18+ 17+ 17+ 17+ 16+ 15= 100)

=100*100

= 10000

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Correct Question:

Refer to the data. If all the firms in the industry merged into a single firm, the Herfindahl index would become: A. 100. B. 1,000. C. 10,000. D. 100,000.

As per the given line segments, the work done by the particle is 78N.

Line segments:

In meth, then bounded by two distinct points on a line is called as line segment.

Given,

Here we have a particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field below.

And we need to find the work done.

While we have the function in the given question as,

=> F(x,y,z) = z²i + 3xy j + 4y²k

Here we have consider that, If C is the path the particle follows, then work done is ∫ₓᵃ F dx.

Then according to the question the force F(x,y,z) = z²i + 3xy j + 4y²k and all four points are in the plane is written as,

z = 1/4 y

So, if S is the at surface with boundary C, so that S is the portion of the plane  over the rectangle is calculated as,

=> D=[0,2] x [0,4].

Then as per the stroke's theorem,

=> ∫∫[2z(0) + 3z(1/4) + 4y]

=> ∫∫3z/4 + 4y

=> [39]₀²

=> 78

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The 90 % confidence interval estimate for the population mean using the student's t-distribution is [ 87.137 , 92.863 ] .

Given :

Suppose that the times to complete an obstacle course are normally distributed with an unknown mean and standard deviation. A random sample of 33 course times is taken and gives a sample mean of 90 seconds and a sample standard deviation of 10 seconds.

a 90% confidence interval estimate for the population mean using the student's t-distribution.round the final answers to two decimal places.

Confidence interval :

CI = X ± Z * s / √n

= 90  ±  1.6449 * 10 / √33

= 90 ± 2.863

= [ 87.137 , 92.863 ]

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Full question:

is in the image uploaded.

The joint probability for events A and B is:

P(A and B) = 0.2072

We know that if two events A and B, each with correspondent probabilities

P(A) and P(B) are independet, then the joint probability (this is the probability that both events happen at the same time) is given by the product between the individual probabilities.

In this particular case we know that:

P(A) = 0.28

P(B) = 0.74

Then the joint probability of A and B is:

P(A and B) = P(A)*P(B) =0.28*0.74

P(A and B) = 0.2072

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The probability that 200 or fewer homes were purchased as investment properties is 0.937. This is calculated using the binomial distribution formula, where n = 600, p = 0.31, and x = 200.

1. The binomial distribution formula for calculating the probability of an event occurring is:

P(x) = nCx * p^x * q^(n-x)

where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1 - p).

2. In this problem, n = 600, p = 0.31, x = 200, and q = 1 - 0.31 = 0.69.

3. Plugging these values into the formula, we get:

P(x) = 600C200 * 0.31^200 * 0.69^400

4. Solving this equation, we get P(x) = 0.937.

5. Therefore, the probability that 200 or fewer homes were purchased as investment properties is 0.937.

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It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

Given that

Ted can remove the trash from a football field in three hours. The same field may be cleared by Jacob in two hours. The scenario can be represented by the equation when they cooperate, where t is the total number of hours needed to clear the field.

We have to find how long will it take ted and jacob to clear the field together.

We know that,

Let the number of hours = t

Ted can clear the field = t/3

Jacob can clear the field = t/2

Together they can clear the field = t/3 + t/2 = 1

3t+2t/6 = 6/6

2t + 3t = 6

5t = 6

t = 6/5

t = 1.2 hours.

Converting

1.2 hours = 1 hour 12 minutes.

Therefore, It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

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