a light is suspended at a height h above the floor. the illumination, i, at a point p is inversely proportional to the square of the distance, r, from the point p to the light and directly proportional to the cosine of the angle theta. assume k is the constant of proportionality. which of the following can be used to represent the illumination at point p? i

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Answer:  m 21=

I got it right on test!

Step-by-step explanation:

Answer:

7 photos on each page

Step-by-step explanation:

63/9 = 7

She puts 7 photos on each page.

The answer is m∠1 = 84°

Step-by-step explanation:

m∠4 = m∠2 so m∠2 = 96°

m∠1 + m∠2 = 360 - m∠4 - m∠2

m∠1 + m∠2 = 360 - 96 - 96

m∠1 + m∠2 = 168

m∠1 = 168/2

m∠1 = 84°

The hypothesis of extinction by the violence between them does not seem true as this is the common nature of the species to fight and this would not be a reason for their extinction.

What is a hypothetical illustration?

How should a hypothetical example be written?

The words or abbreviations "for instance," "for example," "i.e." or "e.g." are frequently used after a hypothetical example, albeit the latter two, as you are probably aware, will only come after a comma and won't initiate a new sentence like "for instance" or "for example."

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Answer:

v = 5(a - gt) or

v = 5a - 5gt  These both mean the same thing

Step-by-step explanation:

1/5 v + gt = a  Subtract gt from both sides of the equation.

1/5 v = a - gt  Multiply both sides by 5

v = 5(a - gt)

Answer:

(4), -5/6

Step-by-step explanation:

[tex]13-36x^2-13=-12-13\\-36x^2=-25\\\frac{-36x^2}{-36}=\frac{-25}{-36}\\x^2=\frac{25}{36}\\x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}[/tex]For x^2 = f(a), x = f(a), -f(a)

[tex]x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}\\\sqrt{\frac{25}{36}}\\\sqrt{25}\\\sqrt{5^2}=5\\=\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}=6\\=\frac{5}{6}[/tex]

Reverse the same equation from the negative side

[tex]=-\frac{\sqrt{25}}{\sqrt{36}}\\\sqrt{25}\\=\sqrt{5^2}\\=5\\=-\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}\\=6\\=-\frac{5}{6}[/tex]

Therefore,

[tex]x=\pm\frac{5}{6}[/tex]

The explicit formula, for the arithmetic sequence 3, 7, 11, 15,... is an = 4n - 1

An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

For the arithmetic sequence,

3, 7, 11, 15,...

a = 3,

d = 7 - 3 = 4

So, an = a + (n - 1)d

an = 3 + (n - 1)4

an = 4n - 1

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Answer: -17

Step-by-step explanation:

-3^2 + -5^2/ -3 - (-5)

-34 / -3 - (-5)

-34/2

-17

answer: 180

first I multiplied -4 with 45, which gave me -180, then I made 180 positive by multiplying it with -1

The area of the region enclosed by the curves y = 7sin x and y = sin(7x) , 0 < x < π is 13.7 square units.

Given the equation of the curves:

y = 7sin x and y = sin(7x)

Now, we have to find the area between the curves .

Area between y = 7sin x and y = sin(7x) ,

   A = ∫[7sin(x) - sin(7x)]dx

⇒ A = [-7cos(x) + 1/7 cos(7x)]

⇒ A = [-7cos + 1/7 cos(7)] - [-7cos(0) + 1/7 cos(0)]

Since cos(π) = -1  ;  cos(7) = -1  ; cos(0) = 1

⇒A = [-7(-1) + 1/7 * (-1)] - [-7 * 1 + 1/7 * 1]

⇒A = 7- 1/7 + 7 - 1/7

⇒A = 14 - 2/7

⇒A = 96/7

⇒A = 13.7 units

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The points where the graph intercepts the x-axis is the root of the function.

from the graph the points are 3.9 and 6.1

The vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )^2 + k

y = a ( x - 5 )^2 + {-4)

substituting point ( 4, -1 ) from the graph we have:

-1 = a ( 4 - 5 )^2 - 4

-1 = a - 4

a = 3

substituting the known values to y = a ( x- h ) + k

y = 3 ( x - 5 )^2 - 4

y = 3 ( x - 5) ( x - 5 ) - 4

y = 3 ( x - 5) ( x - 5 ) - 4

y = 3 ( x^2 - 10x + 25 ) - 4

y = 3x^2 - 30x + 75 - 4

y = 3x^2 - 30x + 71

The points where the graph intercepts the x-axis is the root of the function.

from the graph the points are 2 and 4

The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )^2 + k

y = a ( x - 3 )^2 + 2

substituting point ( 0, -16 ) from the graph we have:

-16 = a ( 0 - 3 )^2 + 2

-16 = a - 9 + 2

-16 = a - 7

a = -9

substituting the known values to y = a ( x- h ) + k

y = -9 ( x - 3 )^2 + 2

y = -9 ( x - 3) ( x - 3 ) + 2

y = -9 ( x - 3) ( x - 3 ) + 2

y = -9 ( x^2 - 6x + 9 ) - 4

y = 3x^2 - 54x - 81 - 4

y = 3x^2 - 54x - 85

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[tex] \large \bf \implies{15}[/tex]

[tex]\bf \longrightarrow((2 + 4 \times 2) - 5) \times 3[/tex]

Step 1) ; Calculate the product or quotient

[tex]\bf \longrightarrow((2 + 8) - 5) \times 3[/tex]

Step 2) ; Calculate the sum or difference

[tex]\bf \longrightarrow(10 - 5) \times 3[/tex]

Step 3) : Calculate the sum or difference

[tex]\bf \longrightarrow5 \times 3[/tex]

Step 4) : Calculate the product or quotient

[tex]\bf \longrightarrow15[/tex]

The mathematical expression can be written as [tex]5(x+7)-4^3[/tex]

Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression). Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.

We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.

The algebraic properties most frequently utilized to simplify algebraic statements are associative, commutative, and distributive.

Here the quantity x is increased by 7 and the sum is multiplied by 5.

so we get 5(x+7).

Now 4 cubed is subtracted from the resulting expression.

Therefore the expression looks like [tex]5(x+7)-4^{3}[/tex] .

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1 hour & 45 minutes is the distance between his home and school.

What is distance short answer?

d=rt

distance = rate of speed times time

d= 33X = 44(7/4-X)

33X = 77- 44X

77X = 77

X = 1 hour

33X = 33 miles

44(7/4 - 4/4) = 33 miles each way

1 hour & 45 minutes = 1 3/4 hours or 7/4 hours

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The coordinates of ABC are respectively (-1/3,1), (4/3,2/3), and  (0/3,5/3) .

Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).

If we are given the dilated point, then we can find the original point by dividing by the scale factor.

Triangle ABC was dilated by a scale factor of 3 about the origin mapping it to triangle A'B'C' with vertices A'(-1/3), B'(4/,2), and C(0/-5).

The coordinates of triangle ABC are:

A=(-1/3,3/3) = (-1/3)

B=(4/3,2/3) = (4/3,2/3)

C=(0/3,-5/3) = (0/3,-5/3)

coordinates are formed by two components that are a latitude , giving the north-south position, and a longitude, giving the east-west position.

Therefore the coordinates of ABC are respectively (-1/3,1), (4/3,2/3), and  (0/3,5/3)

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Answer:

10/1 = X

Cross multiply

X = 10

The range of allowable values based on 44 vary by 4.2% is 42.1 to 45.9.

As given in the question,

Value 44 vary by 4.2%  is equal to

4.2% of 44

= ( 4.2 / 100) × 44

= 184.8 /100

= 1.848

≈ 1.9 (nearest tenth)

Range of allowable values based on 44 vary by 4.2% is given by

Lower limit = 44 - 1.9

                 = 42.1

Upper limit = 44+ 1.9

                 = 45.9

Therefore, the range of allowable values based on 44 vary by 4.2% is 42.1 to 45.9.

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's set up some equations based on the information given:

            [tex]\hookrightarrow \text{60 percent of p} = \frac{60}{100} *p=0.6p[/tex]

            [tex]\hookrightarrow \text{'32 less than p'} = p-32[/tex]

Therefore:

    [tex]\hookrightarrow \text{You paid '0.6p' or 'p - 32'}[/tex]

                 [tex]\hookrightarrow \text{The equation is } '0.6p = p-32'[/tex]

                                  [tex]0.6p=p-32\\p-0.6p=32\\0.4p=32\\p = 80[/tex]

Answer:

Hope that helps!

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A new apple orchard is being planted by Aaron's uncle. They plant 12 trees after picking up a truckload of them. They still need to plant 40 trees the following day.

The letter (N) is the symbol used to represent natural numbers. Natural numbers are also known as counting numbers, and they begin with the number 1 and continue to infinity (never ending), which is represented by three dots (...)

900n - 9[tex]n^2[/tex] = A(n) = n(900 - 9n)

For the highest A(n), A'(n) = 0, A'(n) = 900 - 18n = 0, 18n = 900, and n = 900/18 = 50.

50 trees should be planted per acre to produce the most apples possible

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Answer:

The inverse is [-4/3 -5/3 1]

[-4/3 -8/3 1]

[1/3 2/3 0]

Sorry, I didn't know how to type it well.

2√10/3 is irrational number

The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it can be expressed as p/q.

The word "rational" is derived from the word "ratio," which is a fraction and really refers to a comparison of two or more values or integer numbers. It is the ratio of two integers, to put it simply.

Consider the rational integer 3/2. It denotes that the integer 3 is divided by the number 2.

Irrational numbers are those that are not rational in nature. Let's explain; irrational numbers can be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.

After the decimal point, irrational numbers have an infinite amount of non-repeating digits. Here's an illustration of an irrational number:

For instance, 8 = 2.828

MULTIPLYING THE TWO NUMBERS,

2/√18 x 2√5

= 2 /3√2 x 2√5

= 4√5/3√2

= 2√2 x √5 /3

= 2√10/3

rational number multiplied by an irrational number is always a irrational number.

Since √10 is a irrational number, therefore, 2√10/3 is irrational number.

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Yes, it is not possible to have an absolute maximum or absolute minimum.

Here,

We are examining a function over an interval ( a , b ) , for a and b finite,

We have to find,  is it possible not to have an absolute maximum or absolute minimum.

What theorem indicates the existence of absolute maxima or absolute minima of a function?

If f is continuous on a closed interval [a, b] (that is: on a closed and bounded interval), then, the Extreme Value Theorem indicates the existence of an absolute maximum or minimum value of f on the interval [a, b].

Now,

The function is define over an interval (a, b).

Hence, the function is define on open interval.

So, it is not possible to have an absolute maximum or absolute minimum.

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The  entire area under the standard normal distribution curve is always positive even if the z value is negative.

The normal distribution, it's useful to think of the standard deviation as being steps away from the mean. One step to the right or one step to the left is considered one standard deviation away from the mean. Two steps to the left or two steps to the right are considered two standard deviations away from the mean. Likewise, three steps to the left or three steps to the right are considered three standard deviations from the mean.

The probability of the outcome of an experiment is never negative, although a quasi probability distribution allows a negative probability, or quasi probability for some events. These distributions may apply to unobservable events or conditional probabilities.

Therefore,

The value can be negative can be any positive value can be any positive value larger than 1.

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The objective of Exploratory Research research is to gather preliminary information that will help define the problem and suggest hypotheses.

Exploratory Research is a methodology approach that explores research

question that have not previously been studied in depth.

The nature of experimental studies is generally frequently qualitative. However, an investigation with a big sample size might also be quantitative. Due to its open-mindedness and flexibility, it is additionally commonly referred to as interpretivism or a grounded theory method.

It is commonly employed when the subject you're examining is new, or perhaps the data collection method is challenging in certain way.

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Three principles of experimental design: Control, Random, Enough.

What is the principle of an experiment?

The guiding principles of experimental designs are randomization, replication, and local control. These recommendations offer a valid test of significance.

What are the three experimental design principles, and can you briefly describe how each one reduces experimental error?

How many experimental design principles are there?

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The the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.

Constant proportionality:

Constant proportionality means the ratio of two proportional values at a constant value.

Directly Proportional:

In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively.

Given,

Suppose that y is directly proportional to x.

And y = kx.

Here we need to find the value of k when the value of x = 10 and the value of y = 30.

And we also need to find the value of y when the value of x = 14.

First, we have to find the value of k by apply the given value of the equation,

=> 30 = k x 10

=> 30 /10 = k

=> k = 3

Now the value of y when the value of x = 14 and the value of k = 3,

Then

=> y = 3 x 14

=> y = 42.

Therefore, the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.

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The price of carrots per ounce is $0.24 .

Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.

The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.

Now it is given that a 2-pound bag of carrots cost $7.68 .

Therefore price per pound of carrots=$7.68÷2

Price per pound=$ 3.84 .

Now we know that 16 ounces make up a pound.

Price of carrots per ounce=  $3.84 ÷16

Price per ounce=  $ 0.24

Therefore the price of carrots per ounce is $0.24

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