I got the 1st one, but I need help with the second one.

Equation of a plane perpendicular to a given line with direction ratios <a, b, c> and passing through a point (x1, y1, z1) is given by: a(x - x1) + b(y - y1) + c(z - z1) = 0.

The slope of the line we're looking for is 1/2 since perpendicular lines have opposite-reciprocal slopes. When we enter the supplied point into the equation y = 1/2x + b and solve for b, we obtain b = 6. The line's equation is therefore y = 12x + 6.

Rearranged, it is -x/2 + y = 6. a plane that is outlined by vectors that are perpendicular to a normal. As a result, when given a vector with the coordinates a, b, and c, we can infer that all planes perpendicular to this vector have the form ax+by+cz=d, and any surface with this form is a plane perpendicular to a, b, and c.

Get a direction vector to the two points first, then get the supplied normal from the plane's equation. The normal is then produced by adding the direction vector to the normal.

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The size of the payments that need to be made today and in six months are both $ 6, 961.69.

To find the payment that Caitlin needs to make today and in six months, assume this amount of x.

The payment in 6 months would be:

= (13, 000 - x) ( 1 + 2.4 / 100)⁶

The payment today would be x.

Equate them to find the payment:

x = (13, 000 - x) ( 1 + 2.4 / 100)⁶

x = 14, 988 - 1.1529x

x = 14, 987.979 / 2.1529

= $ 6, 961.69

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It is very important to note that this property is only valid for addition and multiplication. If, AC = AB + BC, then AB + BC = AC by the commutative property.

According to the commutative property, a mathematical principle, the product will not be affected by the order in which we multiply the integers. The commutative property of addition states that the sum is unaffected by the order of the addends.

Only addition and multiplication processes can use the commutative property. So, when adding or multiplying any two integers, we can swap the numbers around or modify their order. This is one of the fundamental characteristics of integers.

Adjective. involving, pertaining to, or involving commutation, exchange, substitution, or interchange. Mathematics. Commutative law for multiplication makes reference to the binary operation's property that one term working on another is equal to another term operating on the first, as in a + b = b a.

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Answer:

50 m

Step-by-step explanation:

The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of the top of the tower from the foot of the building is 60. the tower is 50 m high

If in a certain large population of adults. the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

Given data:

Mean = 122

Standard deviation = 5

Sample size = 200

Now let find the the standard deviation of the sampling distribution of the mean sample using this formula

Distribution of sample mean = Standard deviation/√Sample size

Let plug in the formula

Distribution of sample mean = 5 /√ 200

Distribution of sample mean = 5/14.14

Distribution of sample mean = 0.35

Therefore the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

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The required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
From the table,
Mean = ∑fx / ∑f
Mean = 16010 / 100
Mean = 160.10

Standard deviation,
σ = √∑fd²/∑f
σ = √14265/100
σ = 11.94

The required range of weights from one standard deviation, below the mean is given as
= 160.10 - 11.94 ≤ mean

Thus, the required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.

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The two functions such that composition (fog) (x) = H(x) are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

We have a function H(x) = 7 [tex]\sqrt{x-3}[/tex]

We have to find two functions f and g such that (fog) (x) = H(x).

Let f(x) = 7x

g(x) = [tex]\sqrt{x-3}[/tex]

The composition of these functions is,

(fog)(x) = f (g(x))

           = 7 . g(x)

           = 7 [tex]\sqrt{x-3}[/tex]

           = H(x)

Hence the functions are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

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The expression on being divide by x-1 gives -5 as remainder and quotient (x²-x+2)

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x²-5x+11

Given here: The expression as x³-2x²+3x-7 which is to be divide by x-1

Thus dividing using the long divsion method we get

x-1)x³-2x²+3x-7(x²-x+2

     x³-x²

-________

   0-x²+3x

     x²+x

-________

          2x-7

          2x-2

-__________

             -5

Thus The expression can be written as  x³-2x²+3x-7 =(x-1)×(x²-x+2)-5

Hence, On dividing the given expression by x-1 by long divison method we get the remainder as 2.

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The length of the apothem of a regular hexagon is 4√3

The apothem of a regular hexagon is the distance from the center of the hexagon to the midpoint of one of its sides.

To find the length of the apothem, we can use the formula:

apothem = (side length) / (2 * tan(180/n))

where n is the number of sides of the polygon.

In this case, n = 6 (since the hexagon is regular).

So, to find the apothem of a regular hexagon with a side length of 8 ft, we can plug these values into the formula:

apothem = (8 ft) / (2 * tan(180/6))

This gives

apothem = 8 ft / (2 * tan(30))

Evaluate

apothem = 4√3 ft

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The correct person regarding the classification of quadrilaterals is given as follows:

B. Jamie.

The slopes of each segment are given as follows:

-3 and 1/3.

The multiplication of these slopes is given as follows:

-3 x 1/3 = -1.

As the multiplication of the slopes is of -1, the adjacent sides meet at an angle of 90º, meaning that they are perpendicular, and hence the quadrilateral is classified as a square.

This means that Jamie is correct.

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I watch a total of 11 hours of TV on Fridays and Ellen watches TV for ten hours every day. 

Let's plot how long Manuel watches TV each day, with M, Harry as H, and Ellen as E.

Manuel knows that from Monday to Friday he watches TV for M hours, so the total amount of time he watches TV in his week is 5 * M = 5M.

On Friday and Saturday he watches TV for H hours a day, so the total amount of time he watches TV in a week is H*2 = 2H.

Ellen watches her E hours TV from Friday to Sunday, so the total amount of time she watches TV in a week is her E*3=3E.

In total, they watch her TV 37 hours a week.

5M + 2H + 3E = 37

I watch a total of 11 hours of TV on Fridays.

M + H + E = 11

We also know that the amount of time Ellen spends watching TV on a given day is twice as much as she does on a given day as Manuel spends watching TV.

E=2M

You can substitute the value of E for M into the second expression.

M+H+2M=11

Combining equal terms gives:

3M+H=11

Now that we have two equations, we can solve the unknowns M and H. Substitute the 3M formula for H from the second formula into the first.

5M + 2H + 3(3M + H) = 37

Expanding the right-hand side, we get:

5M + 2H + 9M + 3H = 37

Combining equal terms gives:

14M + 5H = 37

Now that we have equation 14M + 5H = 37, we can solve for H.

H = (37 - 14 eyes) / 5

Then you can substitute the formula for H with respect to M into the formula for H.

H = (37 - 14 eyes) / 5

Finally, we can solve for M using the value of H.

M = (37 - 5H) / 14

We know that H = (37 - 14M) / 5, so we can substitute this formula into the formula for M.

M = (37 - 5((37 - 14M) / 5)) / 14

Expanding and simplifying the right-hand side, we get:

M = (37 - 37 + 70M) / 14

Solving for M gives:

M=5

So Manuel watches TV for 5 hours every day and Harry watches TV for (37 - 5 * 5) / 5 = 2 hours every day.

Finally, we can use the equation E = 2M to find out how many hours Ellen watches TV each day.

E = 2 * 5 = 10

So Ellen watches TV for ten hours every day. 

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Commence at the beginning. The x-coordinate is Negative 3 and 12 units, thus move 3 and 12 units to the right. The difference between 3 and 4 is negative three-half.

A point's exact location on a two-dimensional plane is determined by a pair of numbers called its coordinates. The x and y axes, which are two axes that are at right angles to one another, are known as the coordinate plane's axes. How far along each axis a specific point is located is indicated by its coordinates.

Ordered pairs are a way of describing locations on the coordinate plane. A point's location is revealed by an ordered pair by linking the point's positions along the x-axis (the ordered pair's first value) and the y-axis (the second value of the ordered pair).

To locate points, one uses the numbers on a coordinate grid. Using an ordered pair of numbers, each point may be located.

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Answer:

A within-subject variable is a type of variable in which the same subjects are used to measure multiple levels or conditions of the variable. One example of a within-subject variable would be measuring a person's reaction time to a stimulus both before and after a training intervention.

For example: measuring a person's reaction time to a visual stimulus before and after a training program in which the participant learns to react faster to the stimulus, here reaction time is the within-subject variable.

Answer:

x=16

Step-by-step explanation:

x/2=5+3

x/2=8

x=8×2

x=16

a. The solutions to the system of equations f(x) = g(x) are given as follows: x = 0 and x = 1.

b. The explanation is that they have the same numeric value at these values of x.

A system of equations is composed by multiple equations.

The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.

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The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.

Then the surface area of the triangular prism will be

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

The dimension of the triangle is 13 feet, 5 feet, and 12 feet. And the width of the rectangle is 6 feet.

The surface area of the triangular prism will be given as,

Surface area = 5 x 12 + (5 + 12 + 13) x 6

Surface area = 60 + 180

Surface area = 240 square feet

The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

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The graph can be used to determine the median, quartiles, and other statistical measures.

(a). Class width = (maximum value - minimum value)/ number of classes = (109 - 45)/6 = 9

(b).

Class Limits  Class Boundaries Midpoints  Frequencies  Relative Frequencies  Cumulative Frequencies

45 - 54  44.5 - 54.5  49.5  2  0.0741  2

55 - 64  54.5 - 64.5  59.5  7  0.2593  9

65 - 74  64.5 - 74.5  69.5  17  0.6207  26

75 - 84  74.5 - 84.5  79.5  20  0.7407  46

85 - 94  84.5 - 94.5  89.5  14  0.5185  60

95 - 104  94.5 - 104.5  99.5  7  0.2593  67

(c). Histogram

(d). Relative-Frequency Histogram

(e). The basic distribution shape is right-skewed.

(f). Ogive

The ogive graph is a cumulative frequency plot that shows the number of data values that lie at or below each given value on the x-axis. It is constructed by plotting the cumulative frequencies of each data value on the y-axis against the corresponding data values on the x-axis. The points are then connected using closed line segments to form the ogive graph. The graph can be used to determine the median, quartiles, and other statistical measures.

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The sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee. This uses stratified sampling.

In a stratified sample, researchers divide a population into homogeneous subpopulations called strata (the plural of stratum) based on specific characteristics (e.g., race, gender identity, location, etc.). Every member of the population studied should be in exactly one stratum.

Each stratum is then sampled using another probability sampling method, such as cluster sampling or simple random sampling, allowing researchers to estimate statistical measures for each sub-population.

Researchers rely on stratified sampling when a population’s characteristics are diverse and they want to ensure that every characteristic is properly represented in the sample. This helps with the generalizability and validity of the study, as well as avoiding research biases like under coverage bias.

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Answer: Semi-Conservative, and old.

Step-by-step explanation:

In other words, 3/4 fraction of the bill are for vegetables, while 1 part is for fruit.

Using the data provided in the issue, we can determine what percentage of Marco's bill is made up of veggies. We are aware that fruit and vegetables account for 7/12 of the total bill and make up 1/8 of the total. By deducting the portion of the bill that is for fruit from the portion that is for fruit and vegetables, we can determine the portion of the cost that is for vegetables.

We must identify a common denominator for the two fractions in order to accomplish this. Since 12 and 8 have a denominator of 24, we convert both fractions to have a denominator of 24.

1/8 turns becomes 3/24

7/12 changes to 21/24.

We deduct 3/24 from 21/24 in order to derive the percentage of fruit from the percentage of fruit and vegetables.

21/24 - 3/24 = 18/24

Vegetables make up 18/24, or 3/4, of Marco's bill.

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Answer: 6 2/5

Step-by-step explanation:

32 divided by 5 equals 6 with a remainder of 2.

Answer:4.8×105 g  

Step-by-step explanation:

Answer:

$17.32

Step-by-step explanation:

44 hours

52.5 - 44 = 8.5 hours over time for 1.5x regular pay

assume regular pay is x

so 44x + 8.5 * 1.5x =983.15

44x + 12.75x = 983.15

56.75x=983.15

x=17.324

check to see if it's correct

44*17.324 + 12.75*17.324 = 983.14

Answer:

see below

Step-by-step explanation:

1-1-2017

H 26K

W 24K

Net income 30K

H salary 12K

W salary 10K

remain: 8K shared EQUALLY so each gets 4K extra

Distribution:

30K - H gets12+4 =16K, and W gets 10+4 = 14K

The work energy theorem represented as an equation is ΔW = ΔΕ is appropriate option.

Option D is correct.

A fundamental physics principle known as the work-energy theorem asserts that the amount of work done to an object is proportional to the change in its kinetic energy. To put it another way, the kinetic energy of an object is proportional to the net work done to it.

The work-energy theorem can be expressed as an equation because the change in an object's kinetic energy (W) is equal to the change in its work (W). It states that a change in an object's kinetic energy equals the net work done on it. The conservation of energy is a fundamental physics principle that states that energy cannot be created or destroyed; rather, it can only be transferred or converted from one form to another.

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My student ID is 21444367.

The algorithm states that if the digit in the student ID (from left to right) is an even number, then a 0 is placed in the s column in the corresponding row (from top to bottom). If the digit in the student ID (from left to right) is an odd number, then a 1 is placed in the s column in the corresponding row (from top to bottom). Thus, the result of the algorithm applied to my student ID is s = 01101000.

This can be calculated by multiplying the even digits of the student ID by 0 and the odd digits of the student ID by 1 and then adding them together.

For my student ID, 21444367, the calculation would be:

0 * 2 + 1 * 1 + 0 * 4 + 1 * 4 + 0 * 4 + 1 * 3 + 0 * 6 + 1 * 7 = 01101000.

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The required constant of proportionality for the relationship is 1/2.

As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant. In other words, the cost is directly related to the number of gallons pumped.

Let the relation between x and y is

y = kx

Where k is proportionality constant.

Using the given values of x ad y

1 = k(2)

k = 1/2

So, the constant of proportionality for the relationship is 1/2.

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The required solution is above with the help of matrix generation.

Now, According to the question:

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

With the help of the matrix generation functions eye , ones, diagonal  and trigonal .

Command to generate matrix such as M,N,P,Q

M=6*eye(3)

N= triu (5*ones(3))

P=7*ones (3,2)

Q=diag ([2   3   4])

Therefore, the required solution is above with the help of matrix generation.

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The given question is incomplete, complete question is:

Create matrices with eye, ones, diag and triu Create the following matrices with the help of the matrix generation functions eye , ones, diag and triu. See the on-line help on these functions if required (i.e. help eye)M =[6 0 00 6 00 0 6]N =[5 5 50 5 50 0 5 ]P =[7 77 77 7]Q =[2 0 00 3 00 0 4]

The opportunity cost of scoring a 84 on the economics exam rather than a 76 is 15 points on the History exam.

Opportunity Cost is what a person sacrifices when they choose one option over another. It is calculating by subtracting the return of the best forgone option with the return of the chosen option. The outcome could be beneficial or prejudicial, depending on the case.

In the example (refer to the attached table), if the student chooses to score 94 in the economics exam then the student will get 76 in the History test. Thus, The opportunity cost of getting 94 instead of 77 in the Economics test, implies getting 76 instead of 91 in the History exam. It implies:

Opportunity cost of the History exam = 91-76

Opportunity cost of the History exam = 15

Therefore the opportunity cost of scoring 94 on the Economics exam rather than a 77 is 15 points on the History test.

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Answer:

2 is the scale of dilation