Tell whether the sequence is arithmetic. 0, 102, 201, 304, 403, …

(Pls show work)

Answer:

13.47

Step-by-step explanation:

When put into a calculator it comes up to 13.47125. In this case though, I'm assuming we round to the hundredths place.

Answer:

Should be 13.47125 I could be completely wrong though..

Step-by-step explanation:

I used a calculator

Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Check the picture below.

Answer:

14.1

Step-by-step explanation:

You add all of your numbers up, and then you divide by how many numbers you have.

Answer: He will have ½ pints of milk left

Step-by-step explanation: 1½ + 1½ =3

3½-3=½

The maximum rate of change of f at the point (0, 4) is 28, and it occurs in the direction of the vector (28, 0).

To find the maximum rate of change of the function f(x, y) = 7 sin(xy) at the point (0, 4), we need to compute the gradient vector ∇f(x, y) and evaluate it at the given point.

The gradient vector ∇f(x, y) of a function f(x, y) is given by the partial derivatives with respect to x and y:

∇f(x, y) = (∂f/∂x, ∂f/∂y)

Taking the partial derivatives of f(x, y) = 7 sin(xy):

∂f/∂x = 7y cos(xy)

∂f/∂y = 7x cos(xy)

Now, let's evaluate the gradient vector at the point (0, 4):

∇f(0, 4) = (7(4)cos(0), 7(0)cos(0))

= (28, 0)

The maximum rate of change of f at the point (0, 4) occurs in the direction of the gradient vector ∇f(0, 4) = (28, 0). The magnitude of this vector represents the maximum rate of change, and the direction is given by the direction of the vector.

The magnitude of the gradient vector is √(\(28^{2}\) + \(0^{2}\)) = √(784) = 28.

Therefore, the maximum rate of change of f at the point (0, 4) is 28, and it occurs in the direction of the vector (28, 0).

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Answer:

Step-by-step explanation:

50.24n2

Answer:

C

Step-by-step explanation:

Sin represents opposite/hypotenuse. Thus, when A is the reference angle, 21 is the measure of the opposite side (CB) and 29 is the measure of the hypotenuse (AB).

Cos represents adjacent/hypotenuse. Therefore, when A is the reference angle, 20 is the measure of the adjacent side (AC) and 29 is the measure of the hypotenuse (AB).

Answer:

2/65

Step-by-step explanation:

trust me

The probability that Sam picks two blue pens is,

⇒ 5 / 26

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A box has 26 pens —6 red, 8 green, 5 blue, and 7 black.

Here, Sam picks two pens at a time without replacement.

Hence, We get;

The probability that Sam picks two blue pens is,

⇒ P =  5 / 26

Thus, The probability that Sam picks two blue pens is,

⇒ 5 / 26

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer: The answer to this question is: the mass of the metal in pounds is 1.5 grams.

Step-by-step explanation: Search a free gram to pounds calculator and input your given input or output into there for further help if needed.

Hope this helps

The mass of the metal in pounds is 1.5 pounds.

A unit conversion expresses the same property as a different unit of measurement.

Given that, a scientist measures the mass of a metal to be 682 grams

682 grams = 0.682 kg

0.682 kg = 0.682*2.2 = 1.5 pounds.

Hence, The mass of the metal in pounds is 1.5 pounds.

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Answer:

Cost Function is:

c = 4n

Or, using n as a function variable, we write:

c(n) = 4n

Step-by-step explanation:

c represents total cost
n represents notebook

4 represents cost per notebook

Answer:

I believe the answer is option B because I am right. Haha trust me.

Step-by-step explanation:

The equation that represents the line of best fit for the scatterplot is given as follows:

B. y = -10x + 100.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the graph, we have that:

Hence option B is correct.

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(a) log_3 (11)- log_3 (4)= log_3 (11/4)

(b) log_8 (5) + log_8(7) = log_8(35)

(c) 2log_9 (5) = log_9 (25)

(a) To simplify this expression, we can use the logarithmic identity:

log_b (x) - log_b (y) = log_b (x/y)

Using this identity, we get:

log_3 (11) - log_3 (4) = log_3 (11/4)

Therefore, the given expression simplifies to log_3 (11/4).

(b) Similar to part (a), we can use the logarithmic identity:

log_b (x) + log_b (y) = log_b (xy)

Using this identity, we get:

log_8 (5) + log_8(7) = log_8(5*7)

Therefore, the given expression simplifies to log_8(35).

(c) We can use the exponential form of logarithmic expression to prove this. This states that for any base 'b', if log_b (x) = y, then b^y = x.

Using this definition, we have:

2log_9 (5) = log_9 (5^2)

= log_9 (25)

Therefore, the given expression simplifies to log_9 (25).

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The solution to the equation f(x)=g(x) are x=-2 and x=1.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.

Now, f(x)=g(x)

-x+6=-x²-2x+8

⇒ x²+x-2=0

⇒ x²+2x-x-2=0 (Splitting middle term method)

⇒ x(x+2)-1(x+2)=0

⇒ (x+2)(x-1)=0

⇒ x+2=0 and x-1=0

⇒ x=-2 and x=1

Therefore, the solution for the obtained equation are x=-2 and x=1.

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Using proportions and constant of proportionality, the train always move the same distance and the cost is always the same

Proportion can defined as the comparison between two numbers or ratios. Using proportions, when two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportional relationship between two numbers can be represented as

y = kx

i)

In this question, let's determine if they have the same constant of proportionality.

y = kx

6 = k(2)

k = 3

12 = k(4)

k = 3

Since they have the same constant of proportionality, the train always go the same distance each minute.

ii)

The time travelled in 10 minutes

y = 3x

y = 3(10)

y = 30

The distance in 10 minutes is 30km

b)

Using constant of proportionality to determine if they have a proportional relationship;

y = kx

21 = k(3)

k = 7

42 = k(6)

k = 7

The equation is y = 7x and the constant of proportionality is 7.

The cost for each person is always the same

ii) From y = 7x

63 = 7x

x = 63 / 7

x = 9

The predicted number for a cost of $63 is 9

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The parameterization of the portion of the circular cylinder is :

x = 4 cos(t) cos(theta)
y = ±1/sin(theta)
z = 4 cos(t) sin(theta)
where t varies from 0 to pi/3 and theta varies from 0 to pi/6.

To find a parameterization of the portion of the circular cylinder y2 z2=16 between the planes x=2 and x=6, we can use cylindrical coordinates. Let r be the radius of the cylinder, and let theta be the angle of rotation around the z-axis. Then, we can parameterize the cylinder as:

x = r cos(theta)
y = y
z = r sin(theta)

Since we want the portion of the cylinder between x=2 and x=6, we can set x=r cos(theta) equal to these values:

2 = r cos(theta)
6 = r cos(theta)

Solving for r in each equation, we get:

r = 2/cos(theta)
r = 6/cos(theta)

Since the cylinder has radius sqrt(16) = 4, we know that r must be between 2 and 4. Therefore, we can set:

r = 4 cos(t)

where t is a parameter that varies from 0 to pi/3 (corresponding to theta varying from 0 to pi/6). Substituting this expression for r into the parameterization above, we get:

x = 4 cos(t) cos(theta)
y = y
z = 4 cos(t) sin(theta)

To find the range of y, we can look at the equation y2 z2=16 and substitute the expressions for y and z above:

y2 (4 cos(t) sin(theta))2 = 16
y2 sin2(theta) = 1
y = ±1/sin(theta)

Since theta varies from 0 to pi/6, sin(theta) varies from 0 to 1/2, so y varies from -2 to -∞ and from 2 to +∞. Therefore, we can write the parameterization as:

x = 4 cos(t) cos(theta)
y = ±1/sin(theta)
z = 4 cos(t) sin(theta)

where t varies from 0 to pi/3 and theta varies from 0 to pi/6.

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If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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The first 5 elements of set H, which contains numbers in G that are also elements of F are {4, 16, 36, 64, 100}.

The intersection of two sets has been the set that includes each of the elements which are shared by both sets.

The symbol for set intersection is  "∩''. The intersection, A ∩ B (read as A intersecting B) lists all the items that really are present in both sets and constitute the common elements of A and B for any two sets A and B.

Now, according to the question;

Set G is the set of positive integers divisible by 4, and

Set F is the set of perfect squares;

Then,

G = {4; 8; 12; 16; 20; 24; 28; 32; 36; 40; 44; 48; 52; 56; 60; 64; 68; 72; 76; 80; 84; 88; 92; 96; 100; 104; ...}

F = {1; 4; 9; 16; 25; 36; 49; 64; 81; 100; ...}

So, by the intersection of the sets;

G ∩ F - a intersection of the two sets, that is, what numbers are present in both sets at the same time.

G ∩ F = {4; 16; 36; 64; 100}

Therefore, The first 5 elements of set H, which have the same numbers in G as elements of F are {4, 16, 36, 64, 100}.

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Answer:

0=−11

Step-by-step explanation:

Combine like terms

7

+

3

−

3

=

4

(

−

2

)

{\color{#c92786}{7x}}+3{\color{#c92786}{-3x}}=4(x-2)

7x+3−3x=4(x−2)

4

+

3

=

4

(

−

2

)

{\color{#c92786}{4x}}+3=4(x-2)

4x+3=4(x−2)

2

Distribute

4

+

3

=

4

(

−

2

)

4x+3={\color{#c92786}{4(x-2)}}

4x+3=4(x−2)

4

+

3

=

4

−

8

4x+3={\color{#c92786}{4x-8}}

4x+3=4x−8

3

Subtract  

3

3

3

from both sides of the equation

4

+

3

=

4

−

8

4x+3=4x-8

4x+3=4x−8

4

+

3

−

3

=

4

−

8

−

3

4x+3{\color{#c92786}{-3}}=4x-8{\color{#c92786}{-3}}

4x+3−3=4x−8−3

4

Simplify

Subtract the numbers

Subtract the numbers

4

=

4

−

1

1

4x=4x-11

4x=4x−11

5

Subtract  

4

4x

4x

from both sides of the equation

4

=

4

−

1

1

4x=4x-11

4x=4x−11

4

−

4

=

4

−

1

1

−

4

4x{\color{#c92786}{-4x}}=4x-11{\color{#c92786}{-4x}}

4x−4x=4x−11−4x

6

Simplify

Combine like terms

Combine like terms

0

=

−

1

1

Answer:

x = -11/14

Step-by-step explanation:

7x + 3 - 3x = 4(x-2)

1. Distribute

7x + 3 - 3x = 4x -8

2. Combine like terms

10x + 3 = 4x - 8

3. Continue combining

14x + 3 = -8

4. Subtract 3 from both sides

14x = -11

5. Divide 14 on both sides

x = -11/14 (fraction)

I think I did something wrong but if it's right, I hope it helps a little!

Answer:

x= 121

y = 93

Step-by-step explanation:

90+x+x-28 = 180(linear pair)

or, 2x-62 = 180

or, 2x = 242

so, x = 121

now

y = x-28(veritically opposite)

or, y = 121 - 28

so, y = 93

Answer ; Its answer is 325.

Answer:

I believe is b. and d.

Step-by-step explanation:

2/5 * x = 4

x = 4 : 2/5

1 bag is 2/5 kg.

The customer wants to buy 4 kg. So you need to multiply the single bag for a number that will give you 4 in total.

Here is an example with whole numbers, 8nstead of fraction. if the bag was 2 kg, and you want a total of 4kg. You need to multiply that 2 by a number x to get to your total 4. so you will have 2 * x = 4

That’s why you have 2/5 * x = 4

to isolate x, you need to devide both side by 2/5.

2/5 * x = 4

: 2/5        : 2/5     (Divide both sides by 2/5)

x = 4 : 2/5            

Answer:

3n + 2

Step-by-step explanation:

Answer:

z = 68

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the opposite internal angles

z = 39+29

z = 68

As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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The distribution of the probability of the given data is a Positive Skewed Probability distribution.

Given to us

A spinner is divided into five sections numbered 1 through 5. Juana records the number the spinner lands on for each of the 50 spins. She computes and graphs the relative frequencies for each number

It is a type of distribution in which the distribution has a constant probability, therefore, the probability of each event occurring is equal.

Symmetric distribution is the type of distribution where the left side of the distribution and the right side of the distribution are mirror images to each other, therefore, they are symmetrical.

Negatively Skewed Probability distribution is a type of distribution of the probability where the right side(tail) of the distribution is more concentrated than the right side.

Positive Skewed Probability distribution is a type of distribution of the probability where the left side of the distribution is more concentrated than the right side.

Since in the given graph probability of every number occurring from 2 to 5 is equal to 0.12(12%), while the probability of number 1 occurring is 0.5(50%).

Thus, the distribution of the probability is towards the right end of the graph.

Hence, the distribution of the probability of the given data is a Positive Skewed Probability distribution.

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Answer:b

b b b bb b b b b b b b b b b b b b b b b b b b b  b b b  b  b b b b

Step-by-step explanation: