The table below shows a proportional relationship between y and z.
Y
72
99
153
N
8
11
17
Find the constant of proportionality from y to z.
Express your answer as a fraction in reduced terms.

Answer:

10,000,000,000

Step-by-step explanation:

[tex]10^{10}[/tex]= 10,000,000,000

rounded to the nearest 10th = 10,000,000,000

Answer:

Figure b

Step-by-step explanation:

the sides are equal

The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Rectangular coordinates of a point is written like (x, y, z)

Cylindrical coordinates of a point  is written like (r, θ, z)

Spherical coordinates of a point is written like (p, θ, φ)

First talk about Rectangular vs Cylindrical.

x = rcosθ

y = rsinθ.

z = z

x^2 + y^2  = r^2

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

r^2 = 4+4 = 8.

r = [tex]\sqrt{8}[/tex]

r = 2[tex]\sqrt{2}[/tex]

θ = [tex]tan \inv-1[/tex](y/x) = [tex]tan \inv-1[/tex](2/2) = [tex]tan -1[/tex](1) = 45° = 0.78rad .

z = -1.

So Cylindrical coordinates is (r,θ,z) = ([tex]\sqrt{8}[/tex],0.78,-1).

Now let's us talk about Rectangular vs Spherical Coordinates.

x =  pcosθsinφ.

y= psinθsinφ.

z = pcosφ.

p^2 =  x^2+y^2+z^2.

tanθ = y/x

cosφ = z/p = z/[tex]\sqrt{x^2+y^2+z^2}[/tex].

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

p = [tex]\sqrt{x^2+y^2+z^2}[/tex] = [tex]\sqrt{2^2+2^2+(-1)^2}[/tex] = [tex]\sqrt{9}[/tex] = 3

θ = [tex]tan -1[/tex](y/x) =  0.78rad .

φ = [tex]cos -1[/tex](z/p) = [tex]cos -1[/tex](-1/3) = 1.91rad

So Spherical coordinates is (3, 0.78rad, 1.91rad).

The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Given Question is incomplete, Complete Question here

The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,

To know more about cylindrical and spherical coordinates here.

https://brainly.com/question/4465072

#SPJ4

The expression used to represent the given phrase is given by x =5 and

y = 26 + 8x and value of the given expression when x =5 is equal to

y = 66.

As given in the question,

Given phrase is:

x equal 5

y equals 26 more than the product of 8 and a number x

Required expression to represent the given phrase is:

x = 5

y = 26 + 8x

Value of the expression y = 26 + 8x when x = 5 is given by :

y = 26 + 8( 5 )

⇒ y = 26 + 40

⇒ y = 66

Therefore, the required expression for the given phrase is x =5 and

y=26 +8x , the value of the expression y = 66 when x = 5.

Learn more about expression here

brainly.com/question/14083225

#SPJ4

The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.

In this problem, the data-set is given as follows:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.

Hence the mean is of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.

After the change, the data-set is of:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.

Hence the mean will be of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.

Then the increase will be of:

1065 - 1035 = 30.

The median of a data-set is the middle element of the data-set, the value which:

The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.

More can be learned about the mean and the median of a distribution at https://brainly.com/question/17631693

#SPJ1

The expected value of the random variable b is given as follows:

2.404 books.

The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.

From the histogram given by the image at the end of the answer, the distribution is given as follows:

Then the expected value of the random variable b is obtained as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.

The histogram is given by the image at the end of the answer.

More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440

#SPJ1

Answer:

if you have about an 85 now than you shouldn’t go below a b

Step-by-step explanation:

By using the concept of compact set, it can be proved that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

What is compact set?

A set K is said to be compact if every open cover of K has a finite subcover.

Let K⊆Rn is compact  f:K→R is continuous, and ϵ>0

Let there exist [tex]x_n, y_n[/tex] ∈ K such that |f([tex]x_n[/tex])−f([tex]y_n[/tex])| > n∥[tex]x_n[/tex]−[tex]y_n[/tex]∥+ϵ,

Since K is compact there is a subsequence [tex]x_{nk}[/tex] and [tex]y_{nk}[/tex] of [tex]x_n, y_n[/tex] respectively such that [tex]x_{nk}[/tex] converges to x and [tex]y_{nk}[/tex] converges to y.

So,  |f([tex]x_{nk}[/tex])−f([tex]y_{nk}[/tex])| > [tex]n_k[/tex]∥[tex]x_{nk}[/tex]−[tex]y_{nk}[/tex]∥+ϵ,

Since f is continuous,

We can write

|f(x)−f(y)| > [tex]n_k[/tex]∥x - y∥+ϵ,

This is true for infinite many [tex]n_k[/tex]

So ||x - y|| = 0

|f(x) - f(y)| > ϵ, a contradiction since f is continuous

So,  there is a number A>0 such that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

To learn more about compact set, refer to the link-

https://brainly.com/question/17175854

#SPJ4

Answer: 34.5

Step-by-step explanation:

    To find the constant of proportionality between miles driven and number of gallons used, we will divide the miles driven by the gallons used.

517.5 / 15 = 34.5

1138.5 / 33 = 34.5

1242 / 36 = 34.5

Step-by-step explanation:

the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.

Answer:

f(x) = 3x + 4

f(4) = 3(4) + 4 = 12 + 4 = 16

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 2x - 1  

when you sub in 0 in x and -1 in y, the y-intercept is -1.

Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

Answer: the answer is 72

Step-by-step explanation:

if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240

Now we need to determine 30% of 240 and the procedure explaining it as such

Step 1: In the given case Output Value is 240.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 240 = 100%.

Step 4: In the Same way, x = 30%.

Step 5: On dividing the pair of simple equations we got the equation as under

240 = 100% (1).

x = 30% (2).

(240%)/(x%) = 100/30

Step 6: Reciprocal of both the sides results in the following equation

x%/240% = 30/100

Step 7: Simplifying the above obtained equation further will tell what is 30% of 240

x = 72%

Therefore, 30% of 240 is 72

I hope this helps

Answer:

  72

Step-by-step explanation:

You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.

The 30% you want will be the difference between 80% and 50%:

  80% -50% = 30%

  192 -120 = 72

30% of the same number is 72.

Answer:

12x² + 10xy + 2y²

Step-by-step explanation:

(3x + y)(4x + 2y) =

= 12x² + 6xy + 4xy + 2y²

= 12x² + 10xy + 2y²

Answer:

1/2

Step-by-step explanation:

-1(15+4-27)/16

Add 15 and 4 to get 19.

Now you have -1(19-27)/16

Subtract 27 from 19 to get −8.

-1(-8)/16

Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.

-(-1/2)

Simplify

1/2

Answer:

1/2

Step-by-step explanation:

⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆

Calculate:

-(15 + 4 - 27) / 16

-(19-27)/16

-(-8) / 16

= 8/16

Simplify:

= 1/2

Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.

In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.

Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:

Profit = Revenue - Cost

In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.

Read more on profit here: https://brainly.com/question/13849511

#SPJ1

The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3

Index form of a number can simply be described as that number written in the form of an exponential expression.

The number can also be written as a single number which is raised to another number.

Some rules of indices to note;

Given that;

(8^(5))/(8^(-9))

Then, we have;

8^5-(-9)

8^5+9

Add the powers

8^14

Hence, the value is 8^14

Learn more about index forms here:

https://brainly.com/question/15361818

#SPJ1

The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .

In the question ,

it is given that ,

the angle bisector of the exterior angle of a triangle is parallel to a side .

we have to prove that the triangle will be an isosceles triangle .

In the triangle ABC given below , AB is extended to AD ,

SO , the exterior angle will be angle DAC ,

let AE be the bisector of the the angle .

So , the equal angles are angle DAC and angle EAC .

it is given that AE is parallel to BC , where BC is base .

we know that ,

if any line intersects two parallel lines then every pairs of alternative  Interior angles are same and also their corresponding angles are equal .

Here AE is parallel to BC and line BD intersects them ,

So , angle ABC = angle DAE    ( corresponding angles )

angle ACB = angle EAC   ( alternate angles )

Now , as AE is the bisector of angle DAC ,

we have , angle DAC = angle EAC

So , we get , angle ABC = angle ACB .

In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal

that means , AB=AC

Hence , the given Triangle is an isosceles triangle .

Therefore , it is proved that the triangle ABC is an isosceles triangle .

Learn more about Isosceles Triangle here

https://brainly.com/question/21475560

#SPJ4

a) The experimental units are the Acacia Trees.

b) The treatments carried used are; active beehives, empty beehives and no single beehive.

c) The response variable is the damage that the elephants caused to the trees.

Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.

From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.

The treatments carried out here are the active beehives, empty beehives and no single beehive.

The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.

Read more about Experimental Research Design at; https://brainly.com/question/17009178

#SPJ1

Proportional relationship for the given table is true and is define as

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

As given in the question,

Value of x and y in the given table are :

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.

y / x for all the values of x and y:

First values:

y /x = 6.4 / 25.6

      = 0.25

Second values:

y/x = 18.2/ 72.8

    = 0.25

Third values :

y /x = 19.3/ 77.2

      = 0.25

0.25 is equivalent to One fourth ( 1/4).

Constant of proportionality exist = 0.25 or One fourth.

Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.

The complete question is:

Determine if the table how a proportional relationship.

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

Yes, it is proportional because all y over x ratio are equivalent to one third.

No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.

No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3

Learn more about table here

brainly.com/question/11533874

#SPJ4

Answer: the student forgot to multiple by right side of equation 2 in line 2

Step-by-step explanation: your welcome :)

The missing value if the point is a direct variation is -15

From the question, we have the following ordered pairs

(2, -6) and (5, y)

These ordered pairs are direct variation

A direct variation is represented as

k = y/x

This means that

y/5 = -6/2

Evaluate the quotient

y/5 = -3

Multiply both sides by 5

y = -15

Hence, the value of y is -15

Read more about direct variation at

https://brainly.com/question/6499629

#SPJ1

The equation of the new function is g(x) = 4(2ˣ)

The exponential equation is given as

f(x) = 2ˣ

Then, we have the transformation to be:

Vertically stretch by a scale factor of 4

The scale factor can be represented as k

So, we have

k = 4

The rule of vertical stretch by a scale factor of k is represented a

g(x) = kf(x)

So, we have

g(x) = 4 * 2ˣ

This gives

g(x) = 4(2ˣ)

Hence, the equation is g(x) = 4(2ˣ)

Read more about transformation at

https://brainly.com/question/1548871

#SPJ1

In the context of hypothesis testing, a test statistic is; c. A value, determined from sample information, used to test the null hypothesis.

Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample. The null hypothesis is said to be a hypothesis where no important difference between the random variables

The test statistic is defined as a value that is computed from the sample data that is used when making a decision about whether or not to reject the null hypothesis.

Looking at the options and based on the definitions above, option C adequately describes the test statistic.

Read more about Hypothesis Testing at; https://brainly.com/question/15980493

#SPJ1

This equation x + (x + 1) + (x + 2) = negative 21 will be used.

Let the first Number is x.

We have to take 3 consecutive integers.

second Number is x+1

third Number is x+2.

Sum of these 3 consecutive integers is x+(x+1)+(x+2).

Sum of these 3 consecutive integers is given as negative21.

so we can write  x+(x+1)+(x+2)=negative 21.

by using above equation we can find the value of 3 numbers.

So the final equation will be x + (x + 1) + (x + 2) = negative 21.

Given Question is incomplete, Complete Question here:

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21

To know more about consecutive integers, here:

https://brainly.com/question/2493629

#SPJ4

Answer:

Domain: all real numbers

Step-by-step explanation:

The function is:

[tex] f(x) = \dfrac{2}{9}x^2 + 18x - 216 [/tex]

The domain of a function is the set of values of the x-coordinates of the points of the function.

In this function, there is no restriction on x, so the domain is all real numbers.

Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after