or, 2x+y-5=0 ple 7 Find the co-ordinates of the foot of the perpendicuair drawn from (1, 5) to the line segment joining (1, 1) and (5, 5).​

Define the terms mentioned above:

Experimental terms refer to the set of procedures used to conduct a scientific investigation. These terms include experimental design, data collection, interpretation of results, discussion of theoretical models, and formulation of hypotheses.

These terms are used to describe the research process, from the selection of the topic to the publication of the results. Experimental terms are also used to describe the methods of analysis of the data collected, such as linear regression and analysis of variance.

Define the following terms: ​(a) Experimental unit ​ (d) Factor ​(b) Treatment ​(e) Placebo ​(c) Response variable ​(f) Confounding

(a) Define experimental unit:

A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable

B. A​ person, object, or some other​ well-defined item upon which a treatment is applied

C. Any combination of the values of the factors​ (explanatory variables)

D. An innocuous​ medication, such as a sugar​ tablet, that​ looks, tastes, and smells like the experimental medication

​(b) Define treatment:

A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable

B. The number of individuals in the experiment

C. Any combination of the values of the factors​ (explanatory variables)

Your answer is correct.

D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable

​

(c) Define response variable:

A. An innocuous​ medication, such as a sugar​ tablet, that​ looks, tastes, and smells like the experimental medication

B. The variable whose effect on the response variable is to be assessed by the experimenter

C. The effect of two factors​ (explanatory variables on the response​ variable) cannot be distinguished.

D. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable

​

(d) Define factor:

A. A variable whose effect on the response variable is to be assessed by the experimenter

Your answer is correct.

B. Grouping together similar experimental units

C. An innocuous​ medication, such as a sugar​ tablet, that​ looks, tastes, and smells like the experimental medication

D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable

​

(e) Define placebo:

A. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable

B. Grouping together similar experimental units

C. An innocuous​ medication, such as a sugar​ tablet, that​ looks, tastes, and smells like the experimental medication

D. Using treatments on many experimental units

​

(f) Define confounding:

A. The effect of two factors​ (explanatory variables on the response​ variable) cannot be distinguished.

B. Using treatments on many experimental units

C. Grouping together similar experimental units

D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable

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The answer is the median would not change.

The median of a set of numbers is the middle value when the numbers are arranged in order. It is not affected by outliers or extreme values as much as the mean is.

If the number 1772 was accidentally changed to 1972, this would increase the value of the number and it would become an outlier in the set. To calculate the median, we need to arrange the numbers in order. The new set would be:

1362 1439 1460 1614 1666 1867 1972

The median of this set is 1614, which is the middle value. As you can see, the change from 1772 to 1972 did not affect the median.

Therefore, the answer is the median would not change.

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The answer is the median would not change.

The median of a set of numbers is the middle value when the numbers are arranged in order. It is not affected by outliers or extreme values as much as the mean is.

If the number 1772 was accidentally changed to 1972, this would increase the value of the number and it would become an outlier in the set. To calculate the median, we need to arrange the numbers in order. The new set would be:

1362 1439 1460 1614 1666 1867 1972

The median of this set is 1614, which is the middle value. As you can see, the change from 1772 to 1972 did not affect the median.

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option C is correct, [tex]f(t)=1.36^{t}[/tex] has greatest growth rate.

A relation is a function if it has only One y-value for each x-value.

Growth rates are the percent change of a variable over time

Formula for the exponential growth is,

f(x)=a(1+r/100)ⁿ

where r = rate of exponential growth

a = initial amount

n = duration or time

The greatest growth rate is in the form of percentage.

We have to check for the value which is higher in the given options.

Hence, option C is correct, [tex]f(t)=1.36^{t}[/tex] has highest growth rate.

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The given question is not complete, similar kind of question is attached below.

The solution is Option B.

The probability of drawing a consonant is given by the equation P = 5/7

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of drawing a consonant be represented as P

Now , the equation will be

The total number of letters in the word DECIMALS = 7 letters

The total number of consonants in the word DECIMALS is given by the set A = { D , C , M , L , S }

So , the number of consonants = 5 letters

And , the probability of drawing a consonant P = total number of consonants in the word DECIMALS / total number of letters in the word DECIMALS

Substituting the values in the equation , we get

The probability of drawing a consonant P = 5/7

Hence , the probability is 5/7

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The given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.

What is the identity matrix?

The identity matrix is a square matrix with 1's on the main diagonal and 0's everywhere else. It is denoted as I. The identity matrix has the property that for any square matrix A, the product of A and I is equal to A itself, so I serve as a sort of "do-nothing" matrix.

Yes, this is correct. If a matrix A is invertible, then it means that it has a unique inverse. This implies that the columns of A are linearly independent, as they form a basis for the space. A row equivalent matrix to the identity matrix (A∼I) will have one pivot in each column, indicating that the columns are linearly independent.

Hence, the given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.

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A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.

This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.

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Answer= 6 and 7/y6 this will be the correct answer

The sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.

The formula for the sum of the first n consecutive odd numbers is n^2. This can be proven by induction.

Let n = 2k – 1.

Base case: When k = 1, then n = 2k – 1 = 1. The sum of the first 1 consecutive odd numbers is 1^2 = 1.

Inductive step: Assume that for some k = p, the sum of the first 2p – 1 consecutive odd numbers is (2p – 1)^2.

Now, consider the case when k = p + 1. The sum of the first 2(p + 1) – 1 consecutive odd numbers is:

(2p – 1)^2 + (2p + 1) + (2p + 3) + … + (4p + 1).

This can be written as (2p – 1)^2 + 2(1 + 2 + … + (p + 1)) (2p + 1).

By the sum of an arithmetic sequence, the expression in the parentheses is equal to (p + 1)(2p + 2).

Therefore, the sum of the first 2(p + 1) – 1 consecutive odd numbers is (2p – 1)^2 + 2(p + 1)(2p + 2).

Simplifying, this is equal to (2p + 1)^2.

Therefore, the statement holds for k = p + 1, and by induction, it holds for all positive integers k.

Therefore, the sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.

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Given: A boat is located 324 feet from the base of the cliff.

The distance from the top of the cliff to the boat is 81 more than twice the height of the cliff, or 2h + 81.

We want to find: The height of the cliff, h.

Equations:

h + (2h + 81) = 324 (The height of the cliff plus the distance from the top of the cliff to the boat is equal to 324 feet)

3h + 81 = 324 (Expanding the left side of equation 1)

3h = 243 (Subtracting 81 from both sides of equation 2)

h = 81 (Dividing both sides of equation 3 by 3)

Therefore, the height of the cliff, h, is 81 feet.

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When graphing a function, the input values are the independent variable(s) and the output values are the dependent variable(s).

A graph is a visual representation of a function that helps to understand the relationship between the input and output values of the function. In a graph, the horizontal axis represents the input values, and the vertical axis represents the output values. Each point on the graph represents a single pair of input and output values, and the entire graph represents the entire set of input and output values of the function.

When graphing a function, the input values are the independent variable(s) and the output values are the dependent variable(s).

For example, in the case of a simple linear function such as y = f(x) = 5x + 4, the input value is x, and the output value is y. To create the graph of this function, you would plot a set of ordered pairs (x, y), where x is the input value and y is the corresponding output value.

Similarly, in the case of a multi-variable function such as z = f(x, y), the input values are x and y, and the output value is z. To create the graph of this function, you would plot a set of ordered triples (x, y, z), where x and y are the input values and z is the corresponding output value.

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By the application of the exponential function to the problems we have;

1)  $16187

2) $1346

3)  6774

4) $5670

5)  $ 7233

6) 4%

We have to know that the value of the car can be obtained by the use of the function;

P = Poe^-rt

P = Value at time t

Po = initial value

r = rate of depreciation

t = time taken

P = 44,000e^-0.25*4

P = $16187

2) P= Poe^-rt

P = 1580e^-0.02 * 8

P = $1346

3) P =  Poe^rt

P = 6348e^0.013 * 5

P = 6774

4) A = P(1 + r/n)^nt

A = 5,000( 1 + 0.036/12)^12 * 3.5

A = $5670

5) A = P(1 + r/n)^nt

A = 6,013.53( 1 + 0.0185/4)^4 *10

A = $ 7233

6)  A = P(1 + r/n)^nt

6,520.02 = 4,848(1 + r/2)^6 * 2

6,520.02/ 4,848 = (1 + r/2)^6 * 2

1.34 = (1 + r/2)^12

ln 1.34 = 12ln (1 + r/2)

ln (1 + r/2) = ln 1.34/12

ln (1 + r/2) = 0.024

1 + r/2 = e^0.024

1 + r/2 = 1.02

r/2 = 1.02 - 1

r/2 = 0.02

r = 2 * 0.02

r = 0.04

r = 4%

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Answer:

a. y = 10x

b. 1000 minutes of 16 2/3 hours

Step-by-step explanation:

a.

30 gal / 3 min = 10 gal/min

65 gal / 6.5 min = 10 gal/min

The relation is a direct proportion.

y = kx

The filling rate is the slope which is also the constant of proportionality.

The equation is

y = 10x

b.

y = 10x

10,000 = 10x

x = 10,000/10

x = 1000

The time is 1000 minutes, or 16 2/3 hours.

Analyzing a function's graph will reveal if it is linear or not. When a linear function is graphed, it produces a straight line. In contrast to a linear function, a nonlinear function has some kind of curve.

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The unknown number is -9.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the product of a number and -7 is 63.

Let the unknown number be x.

Now, -7×x=63

-7x=63

x= -9

Therefore, the unknown number is -9.

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dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!) By applying the chain rule, we can calculate the derivative dz/dr.

The derivative of z with respect to r is given by the chain rule:

dz/dr = (∂z/∂x) * (∂x/∂r) + (∂z/∂y) * (∂y/∂r)

Where (∂z/∂x) and (∂z/∂y) are the partial derivatives of z with respect to x and y respectively, and (∂x/∂r) and (∂y/∂r) are the partial derivatives of x and y with respect to r.

Since x = r cos! and y = rsin!, we can substitute these values into the above equation to get:

dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!)

Thus, by applying the chain rule, we can calculate the derivative dz/dr if we know the partial derivatives of z with respect to x and y.

dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!) By applying the chain rule, we can calculate the derivative dz/dr if we know the partial derivatives of z with respect to x and y.

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The probability of drawing a red marble is 2/10 or 1/5.

To determine this:

The probability of drawing a red marble is 2/10 or 1/5. This means that if we randomly select one marble from the jar, there is a 1 in 5 chance that it will be red.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

Probability is an important concept in statistics and mathematics, and it is widely used in many areas such as insurance, finance, and scientific research.

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The probability of drawing a red marble is 2/10 or 1/5.

To determine this:

The probability of drawing a red marble is 2/10 or 1/5. This means that if we randomly select one marble from the jar, there is a 1 in 5 chance that it will be red.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

Probability is an important concept in statistics and mathematics, and it is widely used in many areas such as insurance, finance, and scientific research.

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Answer:

Step-by-step explanation:

Polynomials are mathematical expressions that consist of variables raised to a power and combined with coefficients. The degree of a polynomial is the highest power of the variable in the expression. The number of terms in a polynomial is the number of separate terms that are added together to form the polynomial.

Here are some common examples of polynomials classified by degree and number of terms:

Degree 1, one term: a linear polynomial, such as 3x + 4

Degree 2, one term: a constant polynomial, such as 25

Degree 2, two terms: a quadratic polynomial, such as 3x^2 + 4x + 5

Degree 3, three terms: a cubic polynomial, such as 2x^3 + x^2 + 4x + 7

Degree 4, four terms: a quartic polynomial, such as x^4 + 3x^3 + 4x^2 + 2x + 6

Note that a polynomial with only one term is always a constant polynomial, regardless of its degree

Answer:

its not possible

Step-by-step explanation:

6=14

10 = 22

if ten is 22

how can 20 be 42

The relative frequencies are 0.133, 0.233, 0.167, 0.200 and 0.267

The most popular genre in your class is Romance

From the question, we have the following parameters that can be used in our computation:

C, C, R, R, D, R, H, H, C, A, A, R, A, A, A, R, R,

H, H, H, C, H, A, R, D, D, D, D, H, R

Where

Comedy (C), Horror (H), Drama (D), Action (A), Romance (R).

Using the above as a guide, we have the following:

Movie Genre Frequency

Comedy (C) 4

Horror (H) 7

Drama (D) 5

Action (A) 6

Romance (R) 8

For the relative frequencies, we have

This is the genre with the highest relative frequence

So, we have

Most popular = Romance

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The Average Value of f(x) = (sin x)4^(cos x) for the closed interval 0≤ x≤π/2   is (B) 6/(πln(4))   .

The average value of a function over a closed interval can be found by calculating its definite integral over the interval and dividing by the length of the interval.

The function is : f(x) = (sin x)4^(cos x)  ;

Substituting the values :

we get ;

Average Value is = (1/π/2) × [tex]\int\limits^\frac{\pi }{2} _0[/tex] (sin x)4^(cos x) dx  .

On Simplifying ,

we get ;

Average Value is = [(-2/π)/ln(4) ] (1 - 4)

⇒ 6/(πln(4))

Therefore ,  the average value of the function over the interval 0≤ x≤π/2 is 6/(πln(4)).

What is the average value of f(x) = (sin x)4^(cos x) for the closed interval 0≤ x≤π/2 ?

(A) 3/ln(4)

(B) 6/(πln(4))

(C) 4/ln(4)

D) 8/(πln(4))

(E) 3π/(2ln(4))

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The Expenditure incurred by the mainor school district is $60,000 & inter-period equity is not achieved.

Interperiod equity refers to a government's obligation to disclose whether current-year revenues are sufficient to pay for the services provided that year and whether or not future taxpayers will be required to shoulder the burdens for services previously provided. It also refers to whether current-year revenues are sufficient to pay for the benefits provided that year or whether current citizens deferred payments to future taxpayers.

Thus, The Expenditure incurred by the mainor school district is $60,000 & inter-period equity is not achieved.

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There are 720 positive four-digit integers that satisfy the condition of having no two consecutive digits being multiples of 3.

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Answer:

C!

Step-by-step explanation:

the sides all have the same ratio

8/12 = 10/15 = 14/21 = 2/3

Answer: there is no answer

Step-by-step explanation: if the whole sentence is letters it is not answerable

a) The time for the battery to be 40% charged is given as follows: 48 minutes.

b) The charge in 1 hour and 48 minutes is given as follows: 90%.

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The constant for this problem is given as follows:

k = 10/12 = 30/36 = 5/6.

Hence the equation is given as follows:

y = 5x/6.

The battery will be 40% charged when y = 40, hence:

5x/6 = 40

5x = 40 x 6

5x = 240

x = 240/5

x = 48 minutes.

1 hours and 48 minutes is equivalent to 108 minutes, hence the charge is given as follows:

y = 5 x 108/6

y = 90%.

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Answer:

14+2(3x-1) dived by 2 = 16

Step-by-step explanation:

Answer:

3,x+13 all you have to do is simplify

Answer:

100

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

x = 4 1/3

Step-by-step explanation:

To solve the equation 6x + 64 = 90, we must isolate the variable.

6x + 64 = 90

    -  64  - 64

6x = 26

/ 6   / 6

x = 4 1/3

Answer:

4.3333333 on going so a stop will be 4.3

Step-by-step explanation:

the total 90, minus 64 will give you 26, the divide 26 by 6 which will give you 4.33333

Answer:

Step-by-step explanation:

yes