Compare the slope-intercept and point-slope forms of a linear equation.​

The dimensions required to minimize the cost of fencing is 180ft and 360 ft.

According to question

The cost of fence on opposite side of river is $40.

The cost of fence on other sides of river is $10.

Total yield = 64800 sq. feet

Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.

Area of fence = xy = 64800 sq feet

⇒ [tex]y = \frac{64800}{x}[/tex]

Let C be the cost of making fence.

For cost to be minimum, dC/dx should be equal to zero.

C = 40x + 10y * 2

⇒ C = [tex]40x + 10(\frac{64800}{x})*2[/tex]

⇒ [tex]\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0[/tex]

⇒ [tex]40x^{2} = 20 * 64800[/tex]

⇒ [tex]x^{2} = 32400[/tex]

⇒ [tex]x = 180[/tex]

⇒ [tex]y = \frac{64800}{180} = 360[/tex]

So, the dimensions needed will be 180 ft and 360 ft.

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The equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18.

The equation will be written as,

C = T - 3

18 = T-3

T = 18 + 3

T = 21 years

Therefore, the equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.

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Answer:

8^18

Step-by-step explanation:

8^15

8^−3

=

8^15

8−3

= 8^15− (−3)

= 8^18

The equations for the functions are f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the two given points for f, we can find the slope:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-2)) / (-3 - (-9))

m = -4 / 6

m = -2/3

Let's use the point (-9, -2):

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

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

Multiplying both sides by 3 to get rid of the fraction:

3y + 6 = -2x - 18

3y = -2x - 24

y = (-2/3)x - 8

So the equation for f is:

f(x) = (-2/3)x - 8

To find the equation for g, we can use the fact that the y-intercept is 6 greater than the y-intercept of f. So if the y-intercept of f is b, then the y-intercept of g is b + 6.

f(x) = (-2/3)x - 8

0 = (-2/3)x - 8

2/3 x = -8

x = -12

The x-intercept of both f and g is -12.

Now we can use the y-intercept and x-intercept to write the equation for g. The slope of g is the same as the slope of f, which is -2/3.

y - (b + 6) = (-2/3)(x - (-12))

y - b - 6 = (-2/3)(x + 12)

Multiplying both sides by 3 to get rid of the fraction:

3y - 3b - 18 = -2x - 24

3y = -2x + 3b - 6

y = (-2/3)x + (3/3)b - 2

y = (-2/3)x + b - 2

So the equation for g is:

g(x) = (-2/3)x + b - 2

We know that the x-intercept of g is -12, so we can plug that in and solve for b:

0 = (-2/3)(-12) + b - 2

0 = 8 + b - 2

b = -6

So the y-intercept of g is -6 + 6 = 0.

Therefore, the equation for g is:

g(x) = (-2/3)x - 2

Hence , the equations for f and g are: f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

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The relationship is not a proportional relationship between S and w.

Saving, S, after w weeks, is represented by the equation

S = 50+45w

If y is proportional to x, then

y ∝ x

y =kx

where k is the constant of proportionality.

Here, no constant term and (0,0) satisfies this equation.

The given equation is

S = 50+45w

Here, we have a constant term.

For S=0 and w=0,

0=50+45×0

0=50

Which is not true as 0 ≠ 50.

Since there is a constant term 50 and the equation is not valid for (0,0), therefore, the given relationship is not a proportional relationship.

I hope this answer helps.

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Solve in terms of x.

[tex]y=\frac{5}{x}[/tex]

Multiply by x on both sides to remove it from the denominator.

xy =5

Divide by y to get x by itself

[tex]x=\frac{5}{y}[/tex]

Answer:

x=5/y

Step-by-step explanation:

y=5/x

cross multiplying

yx=5

x=5/y

Answer:

it would be honestly idj

Step-by-step explanation:

im tryin to get point

The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Serena recently began working at the nearby salon. By and large, $58.50 in tips every day. Roseline recently began working at a bank. Since she doesn't get tips, she procures $16.35 60 minutes. The arrangement of conditions {y = 9.85x + 58.50 and y = 16.35x} can be utilized to address how much cash is procured, y, every day for working x hours.

The number of hours Serena and Roseline have to work to earn the same amount of money will be given as,

16.35x = 9.85x + 58.5

6.5x = 58.5

x = 9 hours

The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.

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The percentage increase is 61.36%. If the airline charges an additional $50 baggage fee, the new percentage increase will be 45.68%.

A percentage increase denotes how much a percentage has risen over time. To get at this figure, discover the difference between the original and final values, then deduct it to get the actual sum of the decrease.

The idea of Percentage increase is simply the amount of increase from the original(initial) to the final figure expressed in terms of 100 parts of the original. E.g.  A 10% increase implies that if the original value is divided into 100 parts, the value has increased by an extra 10 parts. So, if the initial value rose by 16%, the value would rise by 16 for every 100 units, and so on.

The formula for calculating the percentage increase can be expressed as:

[tex]\%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]

[tex]\%\ increase= \frac{355- 220}{220}\times 100[/tex]

[tex]\%\ increase= \frac{135}{220}\times 100[/tex]

[tex]\mathbf{=61.36\%}[/tex]

[tex]New \ \%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]

[tex]New \ \%\ increase= \frac{405- 220}{405}\times 100[/tex]

[tex]New \ \%\ increase= \frac{185}{405}\times 100[/tex]

[tex]New \ \%\ increase=\mathbf{45.68\%}[/tex]

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Answer:

When you have the base of 10 and an exponential index of “n”, the powers of 10 says that the resulting number will be 1 followed by “n” number of zeros. So for example, 10 to the 7th represents the same thing as 1 followed by 7 zeros. The result is 10,000,000 (10 million). Multiplying whole numbers by a power of ten would mean that you ...

Answer:

Step-by-step explanation:

45

In a sequence of first term-10 and the 2nd term is 1. the 5th term of this sequence is -17

information given in the question

The 1st term of a certain sequence is -10

the 2nd term is 1

Each subsequent term is obtained by adding the 2 immediately preceding terms

the 5th term of this sequence = ?

Each subsequent term is obtained by adding the 2 immediately preceding terms. This statement means is applied as below

Therefore:

third term

3rd term

= first term + 2nd term

= -10 + 1

= -9

4th term

= 3rd term + 2nd term

= -9 + 1

= -8

5th term

= 4th term + 3rd term

= -9 + -8

= -9 - 8

= - 17

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Answer:

6 gallons

Step-by-step explanation:

40% of 10 is 4 gallons less

10 - 4 = 6 gallons

Answer:

OK, so we know that 50% of the 80 marbles is 40, but we are supposed to find 45% of it, so basically it is 36 marbles he has found, I hope this is right!

Love from Ella

The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]

What is the distance between two points formula?

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.

Solution explained:

First, Write the distance formula:

[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

Now,

Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :

[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex]      Calculate

[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex]                      Calculate

[tex]\sqrt{25 + 36}[/tex]                            Calculate

Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].

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Using the concepts of statistics, we got that  if the per capita death rate increased, then the exponential growth model would decrease the initial population size.

We know very well, the set up of a differential equation relating instantaneous population growth with respect to the time to the per capita population growth rate and the current population size at an arbitrary time is as follows:

dN / dt = rN

Now, we are told that the constant, r, is  per capita population growth rate. N is  current size of the population at some time. "r" is the "organisms added per reproductive period" divided by  total population at that time. For instance, if the 10 rabbits are born per month and the current population is 100 rabbits, then r value  = 0.1.

Hence, the exponential growth model  would decrease the initial population size  if the per capita death rate increased.

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Answer: 16r²s²=(4rs)²

Step-by-step explanation:

[tex]16r^2s^2=\\\\4^2r^2s^2=\\\\(4rs)^2[/tex]

Answer:

x= 3.4

x+2= 5.4

x+3= 6.4

Step-by-step explanation:

Just figured it out :)

Answer:

Step-by-step explanation:

Para determinar el porcentaje, tenemos que dividir el valor por el valor total y luego multiplicar el resultado por 100.

For the given triangle and the measures of the given angle the value of x is equal to -11° .

As given in the question,

For the given triangle,

Let us consider the triangle name ABC,

Where,  m ∠A = x + 51° ,

m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)

m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)

To get the value of x we have,

Sum of all the interior angles of a triangle is equal to 180°

m ∠A + m ∠B + m ∠C = 180°

⇒ x + 51° + 80° + 60° = 180°

⇒ x + 191° =  180°

⇒ x = 180° - 191°

⇒ x = - 11°

Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .

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The smaller number is 9 and the larger number is 18.

According to the question,

We have the following information:

A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.

Now, let's take the larger number to be x and the smaller number to be y.

So, we have the following expressions:

x = 2y ...(1)

x+14 = 4y-4

Putting the values of x from the equation 1:

2y+14 = 4y-4

Adding 4 to both sides of the equation:

2y+14+4 = 4y

2y+18 = 4y

Subtracting 2y from both sides of the equation:

18 = 4y-2y

18 = 2y

Dividing by 2 on both sides:

y = 18/2

y = 9

Now, putting this value in equation 1:

x = 2y

x = 2*9

x = 18

Hence, the smaller number is 9 and the larger number is 18.

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Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.

Given:

The given ratio is 4:5.

To find: We have to divide 72 in this ratio.

To divide 72 in the 4:5 ratio, we must perform the following steps:

The ratio is 4:5.

We can write the number of the ratio as 4x and 5x by multiplying a constant x.

The total ratio is 4x+5x=9x.

So, 9x is equal to 72.

We can write-

9x=72

x=8.

So, putting the value of x we get-

4×8 and 5×8

So, the numbers are 32 and 40.

Thus 72 divides itself as 32 and 40 in 4:5 ratio.

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Answer:

(8, 9 000)

Step-by-step explanation:

The angle the road makes is 3.43°

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

A 6% downgrade means that for every 100 units of horizontal run.

The vertical height decreases by 6 units.

The grade has a downward angle of

tan⁻1(6/100) = 3.43°

Hence, the angle the road makes is 3.43°

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The term for this kind of sample is cluster sampling

Given

that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.

What is cluster sampling ?

Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.

Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.

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The winner received 53 of the 75 votes in the student gov. election according to provided ratio.

What is ratio?

In arithmetic, a magnitude relation shows range times one number contains another.

Main body:

Because the ratio of students who voted for the winner compared to all students who voted is 0.70

we can rewrite this as:

0.70 = 70/100

And, because we know the total number of students who voted is 75 and if we call the number of students who voted for the winner s , we can then write this relationship and solve for s :

[tex]\frac{70}{100} = \frac{s}{75}[/tex]

Multiplying both sides by 75.

75*[tex]\frac{70}{100} = \frac{s}{75}[/tex]*75

s= 75*70/100

s = 5250/100

s = 52.5

s ≈ 53.

Hence ,The winner received 53 of the 75 votes.

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The bearing of the helicopter from B to A is 75.96 degrees

Information from the question

A helicopter leaves A and flies 40 miles due east

the helicopter flies

10 miles due south

Work out the bearing of B from A = ?

The bearing from B to A is worked using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = 40 miles

adjacent = 10 miles

The bearing is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

tan x = 40 / 10

tan x = 4

x = arc tan 4

x = 75.96 degrees

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a) The Probability density function of given uniform distribution example is

F(x) = 1/3.5 for 8.5 < x< 12

Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where

x ---> minimum value and y---> maximum value

Probability density function is a probability function which defines the density of continuous random variable lying between specified range

values. It is denoted by f( a<X<b)

Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.

We have following informations,

weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.

Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.

this implies a = 8.5 , b = 12

F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12

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#Complete Qestion :

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?