Find the equation of the line passing
through the points (2, 1) and (5, 10).
y= [? ]x + [ ]

The correct population should she answered is  is A) 7th graders in the school

To find out the favorite after-school activity of 7th grade students, Ms. Smith should sample the population directly related to the question. In this case, the most appropriate population to sample would be:

A) 7th graders in the school

By sampling the 7th graders in the school, Ms. Smith can directly gather information about their favorite after-school activities. This population consists of the students themselves who engage in the activities, and they would have first-hand knowledge and experience of their preferences.

B) Parents of 7th graders in the school might provide some insights, but they may not accurately represent the activities chosen by the students themselves.

C) Other 7th-grade teachers in the school may have some observations, but it may not reflect the preferences of the entire 7th-grade student population.

D) Sampling all students in the school would be broader than necessary and may not specifically address the favorite after-school activities of 7th-grade students.

Therefore, option A) 7th graders in the school is the most suitable population for Ms. Smith to sample in order to answer her question about the favorite after-school activity of 7th-grade students.

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The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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a) The range containing the middle 95% of scores is given as follows: 6 to 30.

b) The middle 95% of sample means is given as follows: (15.6, 20.4).

By the Empirical Rule, the range containing the middle 95% of scores for a normally distributed variable is within two standard deviations of the mean.

The bounds of the interval are given as follows:

By the Central Limit Theorem, the standard error for the distribution of sample means for samples of size 25 is given as follows:

\(\frac{6}{\sqrt{25}} = 1.5\)

The bounds of the interval are given as follows:

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The expression for the nth term an, for the infinite series s=∑n=1[infinity]an is ∑n=4¹⁶an = 468

We know that the sum of the first n terms of the series is given by sn. Therefore, we can find an expression for the nth term an by taking the difference between successive values of sn:

sn - sn-1 = an

(4-4n²) - (4-4(n-1)²) = an

Simplifying this expression, we get:

an = 8n - 4

Now we can use this expression to find the values of ∑n=1¹⁰an and ∑n=4¹⁶an:

∑n=1¹⁰an = a1 + a2 + ... + a10

= (81 - 4) + (82 - 4) + ... + (8*10 - 4)

= 76

Therefore, ∑n=1¹⁰an = 76.

Similarly,

∑n=4¹⁶an = a4 + a5 + ... + a16

= (84 - 4) + (85 - 4) + ... + (8*16 - 4)

= 468

Therefore, ∑n=4¹⁶an = 468.

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Answer:

54.60

Step-by-step explanation:

42 x 1.3 = 54.60

Answer:

what are your choices for your answers

Step-by-step explanation:

Answer:

3x+6

Step-by-step explanation:

You have to do the rainbow sooo,

3 ⋅ x = 3x

3 ⋅ 2= 6

Put them together equals 3x+6

Hoped I helped! :)

I apologize, I cannot visually perceive or manipulate colors or lines directly. However, if you provide me with the equations of the lines or any additional information about their slopes, I would be more than happy to help you match the slopes with the corresponding lines.

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To match the lines (l1, l2, l3) with their corresponding slopes, we need to assign letters representing the slopes to each set.

Without specific information about the lines l1, l2, and l3, it is not possible to determine the exact slopes or their corresponding letters. In order to match the lines with their slopes, we would need additional details such as the equations of the lines or the coordinates of points on the lines.

The slope of a line represents the rate at which the line changes vertically (y-axis) with respect to the horizontal (x-axis). It is typically denoted by the letter "m" in mathematical notation.

To accurately match the lines l1, l2, and l3 with their respective slopes, we require more information about the lines themselves. Once the equations or coordinates are provided, we can calculate the slopes using the formula for slope, which is the change in y divided by the change in x.

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Step-by-step explanation:

4+7=11

11+(7+4)=22

22+(7+8)=37

Every step 7+4n you must add

The theorem of total probability is a fundamental concept in probability theory that allows us to calculate the probability of an event by considering all possible ways it can occur. It provides a framework for combining conditional probabilities and accounting for different scenarios or conditions.

The theorem of total probability states that if we have a sample space divided into mutually exclusive and exhaustive events (events that cover all possible outcomes and have no overlap), then the probability of an event A can be expressed as the sum of the probabilities of A given each individual scenario or condition multiplied by the probability of each scenario or condition occurring.

Mathematically, the theorem of total probability can be stated as follows:

P(A) = P(A | B₁) * P(B₁) + P(A | B₂) * P(B₂) + ... + P(A | Bₙ) * P(Bₙ)

where A is the event of interest, B₁, B₂, ..., Bₙ are mutually exclusive and exhaustive scenarios or conditions that can occur, P(A | Bᵢ) is the probability of event A occurring given that scenario or condition Bᵢ has occurred, and P(Bᵢ) is the probability of scenario or condition Bᵢ occurring.

In the context of risk assessment, the theorem of total probability allows us to evaluate the risk associated with an event by considering all possible scenarios or conditions that can contribute to that risk. By breaking down the event into different scenarios and calculating the probabilities associated with each scenario, we can assess the overall risk based on the likelihood of each scenario occurring and the impact of the event under each scenario.

For example, in assessing the risk of a particular disease outbreak, we can consider different factors such as the probability of transmission in different populations, the probability of exposure under various conditions, and the probability of developing severe symptoms given exposure. By applying the theorem of total probability and incorporating these probabilities, we can estimate the overall risk of the disease outbreak and make informed decisions regarding prevention and mitigation strategies.

In summary, the theorem of total probability enables us to systematically analyze and quantify risk by considering all relevant scenarios or conditions and their associated probabilities. It provides a comprehensive framework for risk assessment and helps in making informed decisions based on a thorough understanding of the probabilities involved.

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The total amount of cake consumed is calculated by the combined portion of cake consumed by Tom, Vicki, and Ann is 13/16 of the cake.

If Tom, Vicki, and Ann are eating a cake, and Vicki ate 5/16 of the cake, Ann ate 2/8 of the cake, and Tom ate 1/4 of the cake, we can calculate the total amount of cake consumed.

To add fractions, we need to have a common denominator. In this case, we can convert the fractions to have a common denominator of 16.

Vicki's portion: 5/16

Ann's portion: 2/8 = 4/16

Tom's portion: 1/4 = 4/16

Now, we can add up the fractions:

Total portion = Vicki's portion + Ann's portion + Tom's portion

            = 5/16 + 4/16 + 4/16

            = (5 + 4 + 4)/16

            = 13/16

Therefore, the combined portion of cake consumed by Tom, Vicki, and Ann is 13/16 of the cake.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

Option A: 12

Step-by-step explanation:

From the image of the triangle given, we can see that:

XM = ZM

We are given that:

XM = 2x + 2 and ZM = 4x - 8

Thus;

2x + 2 = 4x - 8

Rearrange to get;

4x - 2x = 8 + 2

2x = 10

x = 10/2

x = 5

Thus, XM = 2(5) + 2

XM = 12

Answer:

15

Step-by-step explanation:

Use the distance formula:

\(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

Insert values:

\((-9,7)=(x_{1},y_{1})\\\\(0,-5)=(x_{2},y_{2})\\\\\sqrt{(0-(-9))^2+(-5-7)^2}\)

Two negatives make a positive. Simplify:

\(\sqrt{(0+9)^2+(-5-7)^2}\)

Simplify parentheses:

\(\sqrt{(9)^2+(-12)^2}\)

Simplify exponents:

\(\sqrt{81+144}\)

Simplify addition:

\(\sqrt{225}\)

Find the square root:

\(\sqrt{225} =15\)

The distance between the two points is 15.

:Done

Answer:

ec and  obtuse triangle

Answer:

i think its $0.20

Step-by-step explanation:

 12                 1

------      =   ---------

 2.49          0.20

1 egg = $0.20

Answer:

C. 17

Step-by-step explanation:

3 times 5 is 15 , then you add 15 plus two which equals 17.

Answer:

C. 17

Step-by-step explanation:

In the equation f(5)=3x+2, you substitute 5 for x.

Which makes the equation f(5)=3(5)+2

Simplified f(5)=17 after you multiply 3(5) and add 2.

Hope this helps!

The transfer function H(s) is given by the ratio of the output Y(s) to the input U(s):

H(s) = Y(s)/U(s) = C(sI - A)^(-1)B + D

To find the open-loop transfer function H(s) associated with the given state equations, we need to perform a Laplace transform on the state equations.

The state equations can be written in matrix form as:

ẋ(t) = A*x(t) + B*u(t)

y(t) = C*x(t) + D*u(t)

Where:

ẋ(t) is the vector of state derivatives,

x(t) is the vector of state variables,

u(t) is the input,

y(t) is the output,

A is the system matrix,

B is the input matrix,

C is the output matrix,

D is the feedforward matrix.

Given the system matrices:

A = ⎣

⎡

​

0

0

0

−680

​

1

0

0

−176

​

0

1

0

−86

​

0

0

1

−6

​

⎦

⎤

​

, B = ⎣

⎡

​

0

0

0

1

​

⎦

⎤

​

, C = [100 20 10 0], and D = [0]

We can write the state equations in Laplace domain as:

sX(s) = AX(s) + BU(s)

Y(s) = CX(s) + DU(s)

Where:

X(s) is the Laplace transform of the state variables x(t),

U(s) is the Laplace transform of the input u(t),

Y(s) is the Laplace transform of the output y(t),

s is the complex frequency variable.

Rearranging the equations, we have:

(sI - A)X(s) = BU(s)

Y(s) = CX(s) + DU(s)

Solving for X(s), we get:

X(s) = (sI - A)^(-1) * BU(s)

Substituting X(s) into the output equation, we have:

Y(s) = C(sI - A)^(-1) * BU(s) + DU(s)

Finally, the transfer function H(s) is given by the ratio of the output Y(s) to the input U(s):

H(s) = Y(s)/U(s) = C(sI - A)^(-1)B + D

Substituting the values of A, B, C, and D into the equation, we can calculate the open-loop transfer function H(s).

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Answer:

A coupon for 30%

Step-by-step explanation:

A coupon takes the a certain percentage of a price and subtracts it (a discount). A coupon for 30% off takes 30% of the price which is $60 and subtracts it, same goes for the $20 off coupon. Because a greater percentage is being taken off of the price, the 30% off coupon would save someone more money.

Answer:

Square is the answer

hope it helps u

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Answer: 118

Step-by-step explanation: if x=4 then 4x3 to the 2nd power= 144. 13x2=26

144-26=118

Answer:

The answer is 10

Step-by-step explanation:

1.  4 x 3²  - 13 x 2

2. 4 x 9 - 13 x 2

3. 4 x 9 - 26

4. 36 - 26 = 10

5. = 10

Answer: 4.6

Step-by-step explanation:

GH is equal to 4.6 since it is congruent to JH. GJ is one line, which makes angles GKH and JKH supplementary angles. Since angle GKH = 90, angle JKH must also equal 90, making these triangles similar. However, if you wish to see it done out mathematically, the following explanation is there:

\(a^{2} + b^{2} = c^{2}\)

3.6^2 + HK^2 = 4.6^2

HK^2 = 4.6^2 - 3.6^2

HK^2 = 8.2

HK = 2.86

HK^2 + GK^2 = GH^2

8.2 + 12.96 = GH^2

GH = 4.6

To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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Answer:

81

Step-by-step explanation:

for the volume you just multiple length, height, and depth

Answer: 81.

Step-by-step explanation:

9 x 3 x 3 . LxWxH  brother!

Answer:

-31f - 70 is your answer

Answer:

It is B

Step-by-step explanation:

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

The Value of the horizontal asymptote is 0

What is horizontal asymptote?

The horizontal asymptote of a function y = f(x) is a line y = k and to calculate the horizontal asymptote please substitute \(x=\)±∞. We can also find the vertical asymptote.

now we are given a function

\(f(x)=2(3)^{-x}\)

Now substitute x=±∞ in the equation, as the x in denominator we get

f(x)= 0

This is the value of the horizontal asymptote

Hence the value of horizontal asymptote comes out to be 0

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Answer:

-1/2

Step-by-step explanation:

To find the slope, you use the rise/run method.

To get from one point to another, you would move 1 unit down (rise) and 2 units to the right (left)

The slope would be -1/2

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There is evidence to suggest that the mean annual rainfall for the state of California and the state of New York is different.

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York have been taken. If required, round your answer to three decimal places.

The value of the z-statistic for the difference between the two population means is -9.6150.

The critical value of z at 0.01 level of significance is 2.3263.

The p-value for the hypothesis test is p = 0.000.

As the absolute value of the calculated z-statistic (9.6150) is greater than the absolute value of the critical value of z (2.3263), we can reject the null hypothesis and conclude that the difference in mean annual rainfall for the two states is statistically significant at the 0.01 level of significance (or with 99% confidence).

Therefore, there is evidence to suggest that the mean annual rainfall for the state of California and the state of New York is different.

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The length of the path over the interval 0 ≤ t ≤ π for the curve (sin(6t), cos(6t)) is 6π units.

To find the length of the path, we can use the arc length formula for parametric curves:

L = ∫[a,b] √(dx/dt)^2 + (dy/dt)^2 dt

In this case, the parametric equations are x = sin(6t) and y = cos(6t). Taking the derivatives, we have dx/dt = 6cos(6t) and dy/dt = -6sin(6t).

Substituting these values into the arc length formula, we get:

L = ∫[0,π] √((6cos(6t))^2 + (-6sin(6t))^2) dt

= ∫[0,π] √(36cos^2(6t) + 36sin^2(6t)) dt

= ∫[0,π] √(36(cos^2(6t) + sin^2(6t))) dt

= ∫[0,π] √(36) dt

= 6∫[0,π] dt

= 6[t] from 0 to π

= 6(π - 0)

= 6π

Thus, the length of the path over the interval 0 ≤ t ≤ π for the curve (sin(6t), cos(6t)) is 6π units.

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