If 14 inches of wire cost 42 cents how many inches of wire can be bought with 21 cents

Answer:

The error of their thinking is that they did not convert the equation to slope intercept form, so they assumed that the 2x was the slope. They got the standard form mixed up with slope intercept.

I hope this helps you!

The results of the three cases are listed below:

In this problem we find three cases of composition between two functions, each of which has to be evaluated. The definition of the composition between the two functions f and g is presented below:

f ° g (x) = f( g(x) )                 (1)

Where x is the input variable of the composite function.

In other words, the input of the function f is the output of the function g.

Now we proceed to find the expressions of the each of the two cases:

Case 1

g ° f (x) = g( f(x) )

g ° f (x) = 4 · (2 · x + 2) - 3

g ° f (x) = 8 · x + 8 - 3

g ° f (x) = 8 · x + 5

Case 2

h ° g (- 3 · x) = h [g (- 3 · x)]

h ° g (- 3 · x) = 3 · [4 · (- 3 · x) - 3]

h ° g (- 3 · x) = 3 · (- 12 · x - 3)

h ° g (- 3 · x) = - 36 · x - 9

Case 3

f ° g (- 3) = f( g(- 3) )

f ° g (- 3) = 3 · [2 · (- 3) + 1] + 1

f ° g (- 3) = 3 · (- 5) + 1

f ° g (- 3) = - 15 + 1

f ° g (- 3) = - 14

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The trigonometric function's formula, which simulates the torque (tau) that the weight applied t minutes after Thomas attached it is

[tex]3 Sin (\frac{2\frac{22}{7} }{60} (t-51))[/tex]

The angular speed of the minutes hand is

[tex]w = \frac{2 (\frac{22}{7}) }{60}[/tex] rad/min

Following the application of weight, the torque as a function of time t is,

[tex]t= t_{0} sin (w (t-5) min)\\ = (3 Nm) sin ((\frac{2 (\frac{22}{7} }{60} ) rad/min (t-5) min)[/tex]

[tex]= (3 Nm) sin ( \frac{2 (\frac{22}{7} }{60} (t-5) rad ) \\= 3 sin (\frac{2 \frac{22}{7} }{60} (t-5)[/tex]

Torque, which is also known as the moment of a force, is the propensity of a force to rotate the body to which it is applied. Force (F) x Distance (r) = Torque is how torque is calculated. The distance (r) between the pivot point and the force's action point. A vector quantity is a torque. As a vector quantity, torque always has a direction that is perpendicular to the plane that contains the vectors of force and displacement.

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Answer:

c=(d-4a)/3

Step-by-step explanation:

d=4a+3c, solve for c

d-4a=4a-4a+3c    ==> isolate the 3c by subtracting 4a from both sides

d-4a=3c

(d-4a)/3=3c/3      ==> isolate c by dividing 3 on both sides of the equation

c=(d-4a)/3

Answer:

Hello,

Answer TRUE.

Step-by-step explanation:

a | n is read,  a  divide n.

if a | n => n=a*q

if b | n => b | a*q , since gcd(a,b)=1, b | q ==> b=q*k

n=a*q=a*b*k=(a*b)*k so  a*b | n

Using the concept of division we can find the amount of money each person owes.

Division is one of the fundamental operations used in mathematics which involves breaking a bigger value into smaller groups with the same number of components.

The federal debt =$24 trillion=$24000000

(one trillion=1000000 million)

The value in trillion is converted to million by multiplying by 1000000.

The number of people the amount to be equally distributed= 300 million

Amount of money equally distributed among each person

=[tex]\frac{Total debt amount}{number of people}[/tex]

=[tex]\frac{24000000}{300}[/tex]

=80000

The amount each person owes is $80000

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The cost of each pencil is $2

Algebraic expressions are expressions comprised of variables, terms, factors, coefficients, and constants.

They are also made up of arithmetic operations such as addition, subtraction, multiplication division, etc

From the information given, we have that 'p' represents the cost of each pencil

The equation is represented as;

3p + $5 = $11

collect like terms

3p = $11 - $5

subtract like terms

3p = $6

Make 'p' the subject of formula

p = $6/3

p = $2

Thus, the cost of each pencil is $2

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1/100 < 0.2 < 1/4 is the correct order of the given numbers arranged from least to greatest.

Given that, 1/100, 1/4 and 0.2 and we have to arrange them from least to greatest. So, basically we have to arrange them in ascending order.

1/100 can be written in decimal form as 0.01

1/4 can be written in the decimal form as 0.25

and 0.2 is already in the decimal form.

Now, we have 0.01, 0.25 and 0.2 and we have to arrange them from least to greatest.

Out of 0.01, 0.25 and 0.2, 0.01 is the smallest and 0.25 is the greatest.

0.01 < 0.2 < 0.25

This is the arrangement of the given number in decimal form.

1/100 < 0.2 < 1/4

This is the correct order of 1/100, 1/4 and 0.2 arranged in ascending order.

Therefore, 1/100 < 0.2 < 1/4 is the required answer.

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The value of the car after 6 years will be $7340  .

The Depreciation can be calculated using the formula

A = P( 1 - r/100)ⁿ

where , A = amount , P = principal , r = rate of deprecation , n = time period

In the question ,

it is given that

the value of the car (P) = $28000

rate of deprecation (r) = 20% per year

time period (t) = 6 years

Substituting the values in the Depreciation formula we get ,

Amount = 28000*( 1 - 20/100 )⁶

= 28000*(80/100)⁶

= 28000*(0.80)⁶

= 28000*0.26214

= 7339.92

≅ 7340

Therefore , the value of the car after 6 years will be $7340 .

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Answer: -125

Step-by-step explanation:

√81/9 = 9/3 =3

√4 = 2∧7 = 128

3-128 = -125

The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

The given parameters are:

Number of hours = at least 30 hours a week

This means that

x + y ≥ 30

Also, we have:

The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).

This means that

y ≤ 2x

Substitute y ≤ 2x in x + y ≥ 30

x + 2x ≥ 30

This gives

3x ≥ 30

Divide

x ≥ 10

Substitute x ≥ 10 in y ≤ 2x

y ≤ 2 x 10

Evaluate

y ≤ 20

Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

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Answer:

10 MPH

Step-by-step explanation:

Doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?​

If Doug rowed 3 1/3 miles in 1/3 hour the equation is:

3 1/3x = 1/3

multiply both sides by 3:

3(3 1/3x) = 3(1/3)

10x = 1 hour

Doug rowed 10 MPH

Answer:

10 mile per hour

Step-by-step explanation:

3 1/3 mile = 3.3333333333333333333333333333333 mile

1/3 hour = 0.3333333333333333333333333333333333 hour

divide 3.33333333333333333333333 by 0.3333333333333333333333333
= 3.333333333333333333333333333333333 * 1/.33333333333333333333
= 3.3333333333333333333333333 * 3
= 9.99999999999999999999999
= 10

Answer:

3/5 is bigger

Step-by-step explanation:

if the numerator is the same then the one with the smaller denominator is bigger

Probability of getting a head is 60%

More heads than tails means these possibilities are

2 Heads - 1 Tail

3 Heads - 0 Tails

Probability of 2 Heads and 1 Tail =   C (3,2) (.60) ^2 (.40)  

=3 * (.36) (.40)  

=3 * .144

=3 (144/1000)  

=3 (18/125)

=54/125

Probability of 3 Heads = (.60) ^3

= .6 (.36)

= .216 = 216 / 1000

= 27 / 125

Hence, total probability =   54 / 125 + 27 / 125

= 81 / 125

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Answer:

56 pints hope this helps   Brainliest please

Step-by-step explanation:

Answer:

7 gallons = 56 liquid pints!

Explanation= 1 gallon = 8 pints

The approximate angle will be made by the stairway with the ground is 46.24°.

As we are been given that, the length of the stairway from the ground is 18 feet, under the right angle triangle, that will be the length of the hypotenuse. Next, since the elevation of the top of the stairway from, the ground is 13 feet, which is considered to be the length of the perpendicular of the assumed right angled triangle.

Now, we are asked to find the angle x,

Since, we know  that

                      sin θ = perpendicular/ hypotenuse

So, substituting the required values the desired angle we get is :

                            sin θ = 13/18

                            sin θ = 0.7222

                              θ  = sin ⁻¹ (0.7222)

                                  = 46.2364

                             x  = 46.24

the angle θ or x is 46. 24°.

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The inequality sign have to be flipped when dividing by a negative number.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given statement is the inequality sign have to be flipped when dividing by a negative number.

According to given question we have

A number that is larger when positive becomes "more negative," and thus smaller when negative, and vice versa.

Dividing by a negative number is the same as dividing by a positive number and then multiplying by −1. Dividing an inequality by a positive number retains the same inequality. But, multiplying by −1 is the same as switching the signs of the numbers on both sides of the inequality, which reverses the inequality:

a<b⟺−a>−b.

Ex:

when dividing both sides by a negative number, we reverse the inequality sign.

Take −3x<9

To solve for x, we divide both sides by −3 and get

x>−3.

Therefore, the inequality sign have to be flipped when dividing by a negative number.

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The correct answer is event correlation.

Event correlation is a technique for making sense of a large number of events and pinpointing the few events that are really important in that mass of information. This is accomplished by looking for and analyzing relationships between events.

Event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. So, what is sample space? The entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment

One example of event correlation can occur with intrusion detection. Perhaps there is an employee account that hasn't been accessed for years, and suddenly a large number of login attempts are noticed. That account may start executing suspicious commands.

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The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.

We want to find points of the form (x, y) that are solutions of the inequality:

x*y > 0

Clearly x and y must be different than zero.

So, for example if x = -1, y can be any negative number, for example y= -3

x*y > 0

(-1)*(-3) > 0

3 > 0

This is true.

Now if x  = 1, y must be positive. LEt's take y = 103, then:

x*y > 0

1*103 > 0

103 > 0

Then we have 3 conditions:

The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.

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15 caps are needed so that she can earn $85 in an [tex]8[/tex]hour day.

The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.

For each hour she is compensated $6.50 with $0.45.

For an 8 hour day =6.50 *8 + 0.45x

Let x be the caps and earning is $85

6.50*8+0.45*x=85

=> 52+0.45x=85

=> 0.45x=33

=> x=15 (approx.)

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We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.

Given that,

52 is the quotient of 2080 and 40.

The expression can be represented by

2080/40=52

We divide 2080 as 1200+800+80

(1200+800+80)/40=1200/40+800/40+80/40

(1200+800+80)/40=30+20+2

(1200+800+80)/40=52

An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor. Using number bonds, we may divide the rectangle's enormous area into a number of smaller boxes to simplify the calculation. The product or quotient is then obtained by adding to obtain the area of the entire.

We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.

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The equations which can be solved to determine the coordinates of the other endpoints are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.

It follows from the task content that the equation which can be solved to obtain the coordinates of the other endpoint, K be identified.

Since the coordinates of the midpoint can be determined as follows;

x-coordinate of the midpoint;

x = (x1 + x2)/2; where x1 = 4 and x = -1.

Therefore, -1 = (4 + x2)/2 is the first required equation.

y-coordinate of the midpoint;

y = (y1 + y2)/2; where y1 = -15 and y = 8.

Therefore, 8 = (-15 + y2)/2 is the other required equation.

Ultimately, the required equations are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.

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If a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub

Given,

The total quantity of water in the tub = 8 gallons

The quantity of water draining for every 5 minutes = 6 gallons

The quantity of water draining for every 1 minutes = [tex]\frac{6}{5} =1.2[/tex] gallons

Consider the number of minutes as x

Then the equation for the amount of water in the tub

f(x)= 8 - 1.2x

The number off minutes take to empty the tub = Total quantity of water / Quantity of water draining per minute

=[tex]\frac{8}{1.2}=6.67[/tex] minutes

Hence, if a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub.

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Answer: x=1/8

Step-by-step explanation:

[tex]\displaystyle\\x-\frac{7}{8}=-\frac{3}{4} \\\\ x-\frac{7}{8}+\frac{7}{8}=-\frac{3}{4}+\frac{7}{8}\\\\x=-\frac{3}{4} +\frac{7}{8} \\\\ x=\frac{7}{8}-\frac{3*2}{4*2}\\\\ x=\frac{7}{8} -\frac{6}{8} \\\\x=\frac{7-6}{8} \\\\x=\frac{1}{8}[/tex]

The kind of transformation which converts the graph of f(x)  into the graph of g(x) is vertical shrink .

What is transformation in graph?

A graph transformation is a procedure that modifies an existing graph or graphed equation to create different version of the following graph.

It is given that the functions are :

f(x) = -9(x+6)2 - 3

g(x) = -9(x-4)2 - 3

We know that if we perform transformation that meant the graph of f(x) is transformed into the graph of g(x).

i.e.,

f(x) = -9(x+6)2 - 3

f(x) = -18(x+6) - 3

f(x) = -18x - 128 - 3

f(x) = -18x - 72 - 56 - 3

f(x) = -9(x-4)2 - 3 - 56

f(x) = g(x) - 56

or g(x) =  f(x) + (-56)

So , as we are adding f(x), this suggests that the transformation is one of the vertical shrink type.

Therefore, the kind of transformation which converts the graph of f(x)  into the graph of g(x) is vertical shrink .

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Answer:

A) x = 225 - 7.5p

B) x = 180 millions of gallons

Step-by-step explanation:

A) Make "x" the subject:

[tex]\sf \rightarrow 0.4x + 3p = 90[/tex]

[tex]\sf \rightarrow 0.4x = 90-3p[/tex]

[tex]\sf \rightarrow x = \dfrac{90-3p}{ 0.4}[/tex]

[tex]\sf \rightarrow x = 225-7.5p[/tex]

B) Demand when the price per gallon is $6:

substitute p = 6

[tex]\sf \rightarrow x = 225-7.5(6)[/tex]

[tex]\sf \rightarrow x = 225-45[/tex]

[tex]\sf \rightarrow x =180[/tex]

To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.

Given that,

To one decimal place, round.

A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

We have to find the distance between two points that are AB and EF.

1. The distance between 2 points A and B.

A(-4, 6) and B(3, -7).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-1,x₂=3 and y₁=6,y₂=-7

After substituting we get,

[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]

[tex]\sqrt{16 +163}\\[/tex]

[tex]\sqrt{185}[/tex]

13.601

Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.

2.The distance between 2 points E and F.

E(-6, -5) and F (2, 0).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-6,x₂=2 and y₁=-5,y₂=0

After substituting we get,

[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]

[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]

[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]

[tex]\sqrt{64 +25}\\[/tex]

[tex]\sqrt{89}[/tex]

9.433

Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.

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Answer: y = 3x+1

Step-by-step explanation: If (4,1) is a solution of y = 3x+1, that means if we plugin the respective values of (4,1), we should have an EQUALITY:

1 = 3(4) + 1

1 = 13 , which is wrong, then the point (4,1) is NOT a solution of y = 3x+1.