5. If g = -2 and h = -3 find the value of
a) 7g - 2h
b) 3gh - 4h
c) 2g²-4h²

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.

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.

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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

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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

Answer:

Figure b

Step-by-step explanation:

the sides are equal

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{w}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{2}} \\\\\\ \cfrac{-3+7}{w+4}=\cfrac{1}{2}\implies \cfrac{4}{w+4}=\cfrac{1}{2}\implies 8=w+4\implies 4=w[/tex]

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

Step-by-step explanation: your welcome :)

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.

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Yes there is sufficient evidence that  the alternative hypothesis is;

bag filling machine works incorrectly at the 402 gram setting which is;

H_o ; μ ≠ 402

Null hypothesis; H_o ; μ = 402

Alternative hypothesis; H_o ; μ ≠ 402

The null hypothesis states that there is no difference in the test which is denoted by H_o. However, the sign of null hypothesis is denoted by the signs of = or ≥ or ≤.

Meanwhile, the alternative hypothesis is one that defers from the null hypothesis. This therefore implies a significant difference in the test. Thus, the signs of alternative hypothesis is denoted by; < or > or ≠.

Now, the question we have is a two tailed test. Thus;

The null hypothesis is;

bag filling machine works correctly at the 402 gram setting which is;

H_o ; μ = 402

The alternative hypothesis is;

bag filling machine works incorrectly at the 402 gram setting which is;

H_o ; μ ≠ 402

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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

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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.

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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.

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The correct option regarding the heights of the trees include:

The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. This was illustrated as:

(12 - 5) > (12 - 7)

7 > 5

The mean of tree heights at Yard Works is 8 feet.

The mean of tree height at The Grow Station is 9 feet.

The mean absolute deviation of the tree heights at both yards is 2.

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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.

128 were Daily News readers. 19 read neither while 35 read both. Weekly Gazette A marketing class conducted a survey of 270 shoppers at a mall to find out how many of them read the Weekly Gazette and how many the Daily News.

What is News readers?

150 attendees were surveyed by a marketing class to find out how many read the Weekly Journal and how many the National News. In this section, word problems will be solved using Venn diagrams. The areas of a Venn diagram that indicate quantities as opposed to will have numbers in them. Confidence interval for difference of two formula You may have read statements like the ones below in newspapers, for instance. law in numerous nations.

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12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.

Given that,

A rectangle's length is 4 inches longer than its width. The area of rectangle is equal to 4 inches less than 2 times the perimeter of rectangle.

We have to find what is the length and width of rectangle.

We know that,

Let take length as l and width as w.

l=4w

Area of rectangle is l×w

Perimeter of rectangle is 2(l+w)

So,

l×w=2(2(l+w))-4

l×w=4(l+w)-4

Take l as 4w

4w×w=4(4w+w)-4

4w²=4(5w)-4

4w²=20w-4

4w²-20w+4=0

w²-5w+1=0

w=3

So,

l=4w

l=12

Therefore, 12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.

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Answer:

n > 3

Step-by-step explanation:

2n - 5 > 1

Add 5 on both sides

2n > 6

Divide by two on both sides to isolate n

n > 3

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

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The angular velocity of a person standing on the equator is ω = 1.026 × 10⁻⁴ rad/s

Angular velocity is the number of revolution per second of an object.

Since a planet rotates through one complete revolution every 17 hours and since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. We thus require its angular velocity.

The angular velocity is given by ω = 2π/T where T = period of revolution

Since the planet rotates through one complete revolution every 17 hours, its period, T = 17 hours = 17 h × 60 min/h × 60 s/min = 61200 s

So, substituting the period into the equation for the angular velocity, we have

ω = 2π/T

ω = 2π/61200 s

ω = π/30600 s

ω = 0.0001026 rad/s

ω = 1.026 × 10⁻⁴ rad/s

So, the angular velocity is ω = 1.026 × 10⁻⁴ rad/s

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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 .

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Step-by-step explanation:

b.) 8/7≈ 1.1

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

It takes 51.33 min or 6/7 hrs to travel upstream 4 km.

What is relative velocity?

it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.

speed of boat = 7 km/hr

speed of river = r km/hr

speed upstream = 7-r km/hr

speed downstream = 7+r km/hr

time taken to go upstream 4 km = 4/(7-r)

time taken to go downstream 8 km = 8/(7+r)

as time taken is equal in both scenario:

4/(7-r) = 8/(7+r)

on solving we get:

r = 7/3 km/hr

put this value in time taken for upstream

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

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Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

Think about two trains that are traveling in the same direction and at the same pace.

Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.

The other train seems to be moving at a constant speed.

So, we know that:

Speed of boat = 7 km/hr

Speed of river = r km/hr

Now,

Speed upstream = 7-r km/hr

Speed downstream = 7+r km/hr

Time taken to go upstream 4 km = 4/(7-r)

Time taken to go downstream 8 km = 8/(7+r)

As the time taken is equal in both scenarios:

4/(7-r) = 8/(7+r)

On solving we get:

r = 7/3 km/hr

Put this value in time taken for upstream as follows:

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

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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,

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Answer:

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

Step-by-step explanation:

Answer:

12x² + 10xy + 2y²

Step-by-step explanation:

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

= 12x² + 6xy + 4xy + 2y²

= 12x² + 10xy + 2y²

Step-by-step explanation:

b.) 8/7≈ 1.1

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

Answer:

Step-by-step explanation:

y = 2x - 1  

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

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.

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The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.

The diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.

In this problem, the diameter tells us about the length of the each quantity.

The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.

Comparing both values

Dime = 17.91mm

Hair = 6.0*10^-2

Divide both quantity together.

17.91 / 6.0*10^-2 = 298.5≅299

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