Which equation represents the values in this table

The appropriate null hypothesis is (b) Flavor preferences are evenly distributed across all flavors

The distribution of the gum flavors is given as:

The sample size is given as:

Sample = 80

From the distribution of the gum flavor, we can see that the count of each flavor are not equal i.e. uneven

This means that we can use the following statement as the null hypothesis:

Flavor preferences are evenly distributed across all flavors

Hence, the appropriate null hypothesis is (b)

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Answer:

y=2x+7

Step-by-step explanation:

2x-y=-7

add y to each side

2x=-7+y

add 7 to each side

2x+7=y

and just flip the sides to make it look nice

y=2x+7

hope this helps :)

(a) the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

(b) the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

What is riemann sum?

A Riemann sum is a method used in calculus to approximate the area under a curve or the value of an integral. It involves dividing the region under the curve into smaller subintervals and approximating the area of each subinterval using a specific rule.

To find the Riemann sum using left endpoints and n equals 4, we need to divide the interval [2, 14] into four equal subintervals. The width of each subinterval, denoted as Δx, is calculated as (b - a) / n, where b is the upper limit (14) and a is the lower limit (2).

So, Δx = (14 - 2) / 4 = 12 / 4 = 3.

Now, we evaluate the function at the left endpoint of each subinterval and multiply it by the width (Δx).

The left endpoints for n = 4 are: x₀ = 2, x₁ = 5, x₂ = 8, x₃ = 11.

The Riemann sum using left endpoints is given by:

L₄ = f(x₀) Δx + f(x₁) Δx + f(x₂) Δx + f(x₃) Δx.

Now, let's substitute the given function f(x) = 2x² + 4x + 2 into the Riemann sum equation:

L₄ = (2x₀² + 4x₀ + 2) Δx + (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx.

L₄ = (2(2)² + 4(2) + 2) (3) + (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3).

L₄ = (8 + 8 + 2) (3) + (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3).

L₄ = (18)(3) + (72)(3) + (162)(3) + (288)(3).

L₄ = 54 + 216 + 486 + 864.

L₄ = 1620.

Therefore, the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

To find the Riemann sum using right endpoints and n equals 4, the process is similar. However, this time we evaluate the function at the right endpoint of each subinterval.

The right endpoints for n = 4 are: x₁ = 5, x₂ = 8, x₃ = 11, x₄ = 14.

The Riemann sum using right endpoints is given by:

R₄ = f(x₁) Δx + f(x₂) Δx + f(x₃) Δx + f(x₄) Δx.

Substituting the function into the Riemann sum equation:

R₄ = (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx + (2x₄² + 4x₄ + 2) Δx.

R₄ = (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3) + (2(14)² + 4(14) + 2) (3).

R₄ = (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3) + (392 + 56 + 2) (3).

R₄ = (72)(3) + (162)(3) + (288)(3) + (450)(3).

R₄ = 216 + 486 + 864 + 1350.

R₄ = 2916.

Therefore, the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

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The events are mutually exclusive events, so P(A|B) is 0.

In this question,

If two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then

⇒ A ∩ B = 0

Now the conditional probability, P(A|B) = \(\frac{P(A \cap B )}{P(B)}\)

⇒ \(\frac{0}{0.10}\)

⇒ 0.

Hence we can conclude that the events are mutually exclusive events, so P(A|B) is 0.

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The sample size should be 24.

What is the sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Here, we have

Given

Margin of error = 300

confidence level = 0.9

standard deviation = 900

Assuming the standard deviation to be of population

ME = Z(0.1/2) × σ/√n

300 = 1.645 × 900/√n

n =  {(1.645 × 900)300}²

n = 24

Hence, the sample size should be 24.

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Answer:

27/220

Step-by-step explanation:

With regards to the above, Pita would have to pick 2 pound coins and 1 50p coin to get £2.50

Then, the probability of picking 1 pound then 1 pound, then 50 Pound

= 3/12 × 2/11 × 9/10

= 9/220

It therefore means that the number of arrangement possible of 2 pounds and 1 50 pounds

= £ - £ - 50 , £ - 50 - £ and 50 - £ -£

= 3

Hence, the required probability

= 3 × 9/220

= 27/220

Answer: 24.7 square cm

Step-by-step explanation:

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Determine for which value(s) of λ the planes U and V are: (a) orthogonal, (b) Parallel.The equation of plane U is given as λx+5y−2λz−3=0. The equation of plane V is given as

−λx+y+2z+1=0.To determine whether U and V are parallel or orthogonal, we need to calculate the normal vectors for each of the planes and find the angle between them.(a) For orthogonal planes, the angle between the normal vectors will be 90 degrees. Normal vector to U = (λ, 5, -2λ)

Normal vector to

V = (-λ, 1, 2)

The angle between the two normal vectors will be given by the dot product.

Thus, we have:

Normal U • Normal

V = λ(-λ) + 5(1) + (-2λ)(2) = -3λ + 5=0,

when λ = 5/3

Therefore, the planes are orthogonal when

λ = 5/3. For parallel planes, the normal vectors will be proportional to each other. Thus, we can find the value of λ for which the two normal vectors are proportional.

Normal vector to

U = (λ, 5, -2λ)

Normal vector to

V = (-λ, 1, 2)

These normal vectors are parallel when they are proportional, which gives us the equation:

λ/(-λ) = 5/1 = -2λ/2or λ = -5

Therefore, the planes are parallel when

λ = -5.(1.2) Find an equation for the plane that passes through the origin (0,0,0) and is parallel to the plane −x+3y−2z=6The equation of the plane

−x+3y−2z=6

can be written in the form

Ax + By + Cz = D where A = -1,

B = 3,

C = -2 and

D = 6. Since the plane we want is parallel to this plane, it will have the same normal vector. Thus, the equation of the plane will be Ax + By + Cz = 0. Substituting the values we get,

-x + 3y - 2z = 0(1.3)

Find the distance between the point

(−1,−2,0) and the plane 3x−y+4z=−2.

The distance between a point (x1, y1, z1) and the plane

Ax + By + Cz + D = 0 can be found using the formula:

distance = |Ax1 + By1 + Cz1 + D|/√(A² + B² + C²)

Substituting the values, we have:distance = |3(-1) - (-2) + 4(0) - 2|/√(3² + (-1)² + 4²)= |-3 + 2 - 2|/√(9 + 1 + 16)= 3/√26Therefore, the distance between the point (-1, -2, 0) and the plane 3x - y + 4z = -2 is 3/√26.

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Answer: thousandths

9,000

Step-by-step explanation:

Answer: thousandths

Step-by-step explanation:

9,000

Answer:

The Y-intercept is -1

Step-by-step explanation:

M*thway is a pathway to many abilities some considered to be... unnatural

Statement (C) the y-intercept is y=-1 describes the graph of the function.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

\(\rm f(x) = \dfrac{x^2-1}{x^2-2x+1}\)

The above function is a rational function.

The denominator cannot be zero

x² - 2x + 1 ≠ 0

(x - 1)²≠ 1

x ≠ 1

To find y-intercept plug x = 0

f(0) = -1

Thus, statement (C) the y-intercept is y=-1 describes the graph of the function.

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The ferryman should transport the goat first, then return alone to bring the wolf, leaving the goat on the right bank. Finally, he should transport the cabbage and leave it with the wolf.

In order to solve this puzzle, the ferryman must make a series of careful moves to ensure the safety of the wolf, goat, and cabbage. The first step is to transport the goat to the right bank, leaving it there. The ferryman then returns to the left bank alone.

He takes the wolf across the river, but before leaving it on the right bank, he brings the goat back to the left bank. Now, the goat and cabbage are on the same side, while the wolf remains on the right bank.

The ferryman transports the cabbage to the right bank, leaving it there, and then returns alone to the left bank. Finally, he takes the goat across the river one last time, completing the puzzle. This sequence of moves ensures that the wolf and goat are never left alone together, nor are the goat and cabbage.

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If Southland is producing at point X, to determine the number of additional schools it can produce without giving up any movies, we need to refer to the concept of production possibilities frontier (PPF).

The PPF represents the maximum output combination of two goods that an economy can produce with its available resources and technology.

In this case, movies and schools are the two goods being produced. If Southland is operating at point X on the PPF, it means it is efficiently allocating its resources to produce a certain quantity of movies and schools. To find out how many more schools can be produced without sacrificing any movies, we need to identify a point on the PPF that lies on the same movie production level as point X.

Let's assume that at point X, Southland is producing 10 movies. To determine the number of additional schools, we need to find a point on the PPF where the movie production level is also 10. Let's say at this point, Southland can produce 20 schools.

Therefore, the answer is 20 more schools.

If Southland is producing at point X and is currently producing 10 movies, it can produce an additional 20 schools without giving up any movies. This calculation is based on the assumption that the PPF remains constant and there are no changes in resource availability or technology.

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There were 357 dogs that were sold that day.

What is least squares regression line?

The line that best matches a linear connection between two variables in data is called a least-squares regression line because it minimizes the vertical distance between the data points and the regression line.

The given equation is,

y = 0.6p + 10.0

The residual for the day when 520 people attended was 35.

So, p = 520.

Plug 520 in the above equation, we get

y = 0.6(520) + 10.0

y = 312 + 10

y = 322

As, people attended was 35

So,

y = 322 + 35

y = 357

Hence, there are 357 dogs are sold that day.

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Answer:

\(name \: of \: the \: book \\ auther \: of \: book \\about \: auther \: shortly \\ content \: of \: the \: book \\ comparison \: with \: any \: social \: issue \\ relevence \: of \: that \: in \: present \: days \\ important \: peoples \: thoughts \: about \: that \: book \\ ur \: opinion \: about \: it \\ i \: hopethis \: helps \: you\)

Answer:

Depends on the level, you are writing!! Check the pictures below.

Step-by-step explanation:

AccordingAccording to the question probability table of given situation is given as image1 and image2, the probability associated with W = 3 and w = 1 are 8/27 and 12/27 respectively.

Part (a):-

Here, W is the random variable giving the difference between the number of heads and tails in three tosses of a coin.

The sample space on three tosses of a coin along with the corresponding values of W as follows: given below in (image1).

Part (.b)

Here, it is found that the random variable,

W can take the values 3,1,−1,−3.

As the coin is biassed with the probability of heads and tails in the ratio, 2:1, it implies that P(H) =2/3 and P(T) = 1/3.

Here, the probability associated with W = 3, (all three heads) can be calculated as follows:

P(W=3) = ⅔ × ⅔ × ⅔ = 8/27      

Similarly, the probability associated with W = 1, (2 heads and 1 tails) can be calculated as follows:

P(W=1) = 3 × (⅔ × ⅔ × ⅓ ) = 12/27

So, the probability distribution table for W can be calculated as follows: given below in (image2).

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Answer:

The top and the bottom

Step-by-step explanation:

Answer:

#3, the one with the straight line --> linear bc its a constant slope

Answer:

I don't know what z I don't know I don't know

Answer:

Maybe 78 and 76

Step-by-step explanation:

Thats what I got, Idrk how to explain it though-

Answer: Travis studied Spanish for 2.5 hours.

Step-by-step explanation:

1. First, we have to make our equation. Since it DID state that he studied x hours EACH for Spanish, English, and Social Studies, we could just make that 3x.

So,

3x + 1.5 + 2.25= 11.25

3x + 3.75= 11.25

-3.75 -3.75

3x/3=7.50/3

x=2.5

Answer:

Answer is -2

Step-by-step explanation:

5.5 minus 7.5 is negative 2. hope this helps.

Answer:

Step-by-step explanation:

Step One

Find the exterior angle connected to the 93 degree angle. It is also a supplement to 93. Supplementary angles add to 180. Call the exterior angle y

93 + y = 180          Subtract 93 from both sides

y = 180 - 93

y = 87

Step two

Add all the exterior angles. They equal 360

x + 52 + 87 + x + 3 + 78 = 360    Combine the like terms

Step 3

Solve the equation

2x + 220 = 360                            Subtract 220 from both sides

2x  = 360 - 220

2x = 140                                        Divide by 2

x = 70

I don't see that anywhere, but I'm pretty sure I'm right.

Answer: 70

Step-by-step explanation:

Since triangle PQR is similar to triangle PTS

1) Side PQ is similar to side PT

2) Side QR is similar to side TS

3) side PR is similar to side PS

Answer:

a

Step-by-step explanation:

Answer:

I'm not really sure but i think it is A

The total number of possible ways to complete the test would be 2048.

Total number of questions = 11

Each equation has two possible answers (either true or false).

We need to find the total number of ways in which the test can be​ completed.

the total number of possible ways to complete the test= 2×2×2×2×2×2×2×2×2×2×2

the total number of possible ways to complete the test=

2¹¹

Therefore the total number of possible ways to complete the test is 2048.

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The predicted leaf weight in the percent which is left after 80 days is equal to 67.03%.

Number of days after which predict the percent leaf weight left = 80 days

Experimentally determined k-value =  0.005,

Use the exponential decay model for leaf litter decomposition,

W(t) = W0 × e^(-kt)

where W(t) is the predicted percent leaf weight remaining at time t,

W0 is the initial percent leaf weight at time 0,

k is the decomposition rate constant,

And e is the mathematical constant approximately equal to 2.71828.

Using the given k-value of 0.005

And assuming an initial weight of 100%,

Plug in the values to get,

⇒ W(80) = 100 × e^(-0.005×80)

⇒ W(80) = 100 × e^(-0.4)

⇒ W(80) ≈ 67.03

Therefore, the predicted percent leaf weight left after 80 days is approximately 67.03%.

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Answer:

B

Step-by-step explanation:

f=120p

f=120(16)

f= 1920

The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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From the figure, the lines parallel to AE are DH, CG, and EF.

Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.

If two straight lines are in the same plane and never intersect, they are said to be parallel lines.

So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.

As equidistant lines, they are always the same distance apart.

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Answer:

Step-by-step explanation:

You need to use vertex form of a quadratic to solve this.

Consider the vertex to be \((h,k)\)

Another way of representing a quadratic is in "vertex form":

\(f(x) = a(x-h)^2+k\)

Now all you have to do is solve for a.  You know that the vertex is \((0,2)\) and you have know the point of \((1,8)\).  Now, all you have to do is plug in these values and solve for a.

\(8 = a(1-0)^2+2\\8=a(1)^2+2\\8=a+2\\a=6\)

Now you know the equation is \(f(x) = 6(x-0)^2+2\) , but you need it in quadratic form.  All you have to do is solve is distribute the 6:

\(6x^2+2\)

You get:

a = 6

b = 0

c = 2

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