Part 2: The xy-Plane
Use these two graphs to answer questions 4 and 5.

4. Do these graphs represent functions? Explain.

Answer:

SS: $3,602.20

M: $842.45

Step-by-step explanation:

58100 x 0.062 = 3,602.2

58100 x 0.0145 = 842.45

Answer:

  2 points: b, d

Step-by-step explanation:

Given the graph of a cubic function, you want to know the number of relative extreme points.

A point is a relative extreme if the points on either side of it are both less than or both greater than the extreme point. A relative extreme is a peak point or valley point on a graph, a point where the slope is zero, and changes sign from one side of the point to the other.

The relative extremes on the given graph are labeled 'b' and 'd'. There are two relative extremes.

__

Additional comment

Point 'b' is a relative minimum, where the slope changes from decreasing to increasing, and adjacent points are more positive. Point 'd' is a relative maximum, where the slope changes from increasing to decreasing, and adjacent points are more negative.

An "absolute extreme" is a relative extreme such that no points anywhere on the graph are more extreme.

The number of relative extremes a polynomial graph may have is 1 less than the degree of the polynomial. This can help you determine the degree from the number of extremes, or the number of extremes from the degree.

(a) The deposit that Kyla paid is $3000  

(b) the balance inclusive of the interest is $10080    .

In the question ,

it is given that ,

the price of the furniture set = $12000

Part (a)

percent of deposit that Kyla paid = 25% ,

that means the amount paid by Kyla as deposit = 25% of 12000

= 0.25 × 12000

= 3000

So , Kyla deposited $3000 .

Part (b)

the balance amount = price of furniture - amount deposited ,

the balance amount = 12000 - 3000

= 9000

and the rate of interest = 12% ,

So , the interest paid = 12% of balance amount

= 12% of 9000

= 0.12 × 9000

= 1080

So , the balance amount inclusive of interest = 9000 + 1080

= $10080

Therefore , (a) The deposit that Kyla paid is $3000  

(b) the balance inclusive of the interest is $10080    .

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The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

6 persons for 40 dresses;

So, here

The numerator is 6;

and,

The denominator is 40;

So, The fraction that will be formed is: [tex]\frac{6}{40}[/tex]

In order to simplify to the simplest form, we have to divide it by the common divisor of 6 and 40.

So,

The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]

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Answer:

29/8 or 3 5/8

Step-by-step explanation:

Michael took his kids to get haircuts. The haircut cost $50 for all of the kids combined. He also gave the stove a 30% tip.  

The total cost of the haircut including the tip was $65.

What do you mean by cost price?

Cost price is the total sum of money that it costs a manufacturer to make a particular good or offer a particular service. The total expenditure needed to create something or perform a service is the cost. The following methods for determining profitability involve cost price: Profit in monetary terms is calculated as Selling Price (Excluding Tax) – Cost.

Solution Explained:

Given,

Cost of the haircut is $50

Tip that Micheal gave is 30%

So calculating,

Tip = (50 X 30) / 100 = 15

Therefore, the total cost including tip for the haircuts is

= 50 + 15

= 65

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Step-by-step explanation:

from the first line s

y - 7 = 9/10 × (x - 4)

we only need the slope, which is 9/10.

the -7 did not disturb this. only if y had a factor different to 1, we would have to re-simplify the equation to get the slope.

remember, a slope expresses the ratio (y change / x change).

a perpendicular slope note turns the y/x ratio upside-down and flips the sign.

so, 9/10 turns into -10/9, which is the slope of the new line t.

we can use the point-slope form to incorporate the given point and get the y-intercept for the final slope-intercept equation :

y - 6 = -10/9 × (x - -6) = -10/9 × (x + 6) =

= -10/9 × x - 60/9 = -10/9 × x - 20/3

y = -10/9 × x - 20/3 + 6 = -10/9 × x - 20/3 + 18/3 =

= -10/9 × x - 2/3

the line t is

y = -10/9 × x - 2/3

======================================================

Use this formula

a & b/c = (a*c + b)/c

to convert from a mixed number to an improper fraction.

Let's use that formula to find the following

a & b/c = (a*c + b)/c

2 & 1/3 = (2*3+1)/3

2 & 1/3 = 7/3

She has 7/3 yards of material.

Linda wants to make 3 curtains. Each curtain needs 8/9 of a yard.

3*(8/9) = 24/9 = (8*3)/(3*3) = 8/3

Therefore, she needs 8/3 yards of material.

But this is a problem because she needs more material than what she has on hand. In other words, 8/3 > 7/3 since 8 > 7.

-----------

Another way to look at it:

7/3 = 2.333 yards is the approximate amount of fabric she has

8/3 = 2.667 approximately is the total amount of fabric she needs, which is clearly larger than the 2.333 yards she has.

Unfortunately Linda does not have enough fabric to make 3 curtains.

Answer: Graph 4  

Step-by-step explanation: Because "[z]" is greater than the absolute value of 1/2, any number that is not in between -1/2 and 1/2 is [z]. This is also known as an "or" statement for z can be greater than 1/2 "or" less than -1/2.

[Z]>1/2 (Given)

Plug-in points for "z":

[.25] =.25 & -.25   (subs prop of inequality)

-1/2 <.25 < 1/2 This is an "and" statement, where the line would overlap. So this solution is incorrect

Next, try another number

[1] = -1,1

-1/2<1>1/2 This is an "or" statement meaning the solution can be either less than -1/2 or greater than 1/2 So this would be a solution to the problem

The equation that gives the gross weekly pay (p) if you work a hours per week is 11h+78.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.

Here,

2600*3/100=26*3

=78

p=11h+78

The algorithm for calculating gross weekly pay (p) if you work a number of hours per week is 11h+78.

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The value of x using the F.O.I.L method can be determined by the expression: [tex]54x^2-129x-23[/tex]

What is FOIL Method?

FOIL is a mnemonic for the standard method of multiplying two binomials, hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product:

First (“first” terms of each binomial are multiplied together)

Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second)

Inner (“inside” terms are multiplied—the second term of the first binomial and the first term of the second)

Last (“last” terms of each binomial are multiplied)

In the question, It is given:

(6x + 1)°

(9x - 23)°

Now Apply the F.O.I.L Method, to find the value of x;

⇒(6x + 1) (9x-23)  

Remove parenthesis and multiply;

⇒6x×9x+6x×(-23)+1×9x+1×(-23)  

⇒6x x 9x+6 x 23x + 1 x 9x + 1 x 23

Now, we have to simplify the terms,

⇒6x x 9x + 6 x 23x + 1 x 9x + 1 x 23

So after simplification, we get:

[tex]54x^2-129x-23[/tex]

Hence,

The value of x can be determined by the expression: [tex]54x^2-129x-23[/tex]

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Answer:

80/44 = 1.81

The unit rate is $1.81

The simplified exponential expression (z^9z^(-3))^(-2) is given as follows:

1 over z raised to the twelfth power.

The expression for this problem is given as follows:

(z^9z^(-3))^(-2)

The parenthesis takes precedence, hence the first term to be simplified is:

z^9z^(-3)

We have the multiplication of two terms with the same base and different exponents, hence the base z is kept and the addition of the exponents 9 and -3 is of:

9 - 3 = 6.

Hence the simplified part is of:

z^6

Then the expression is:

(z^6)^(-2).

Now we have the power of power rule, in which the base z is kept and then the exponents 6 and -2 are multiplied, as follows:

6 x (-2) = -12.

Then the simplified expression is:

z^(-12).

A negative exponent means that the number can be written into the denominator with a positive exponent, hence:

1/(z^12) = 1 over z raised to the twelfth power.

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The equivalent expression to the given expression 3x - 4 - (5x + 7) with fewer terms is  - 2x - 11.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

3x - 4 - (5x + 7)

Open the bracket

3x - 4 - (5x + 7) = 3x - 4 - 5x - 7

Take likely terms together

3x - 4 - (5x + 7) = 3x - 5x - 4 - 7

Solving to get.

3x - 4 - (5x + 7) = - 2x - 11

Hence "The equivalent expression to the given expression 3x - 4 - (5x + 7) with fewer terms is  - 2x - 11".

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The solutions to the given linear equation are (1, -4), (-9, -12), and (6, 0)

From the question, we are to determine the ordered pairs that are solutions to the given equation

The given equation is

4x - 5y = 24

To do this, we will check for the ordered pairs that satisfy the equation.

(1, -4)

Substitute x = 1 and y = -4

4x - 5y = 24

4(1) - 5(-4) = 24

4 + 20 = 24

24 = 24

Therefore, (1, -4) is a possible solution to the equation

(-9, -12)

Substitute x = -9 and y = -12

4x - 5y = 24

4(-9) -5(-12) = 24

-36 + 60 = 24

24 = 24

Therefore, (-9, -12) is a possible solution to the equation

(4, 8)

Substitute x = 4 and y = 8

4x - 5y = 24

4(4) - 5(8) = 24

16 - 40 = 24

-24 ≠ 24

Therefore, (4, 8) is not a solution to the equation

(6, 0)
Substitute x = 6 and y = 0

4x - 5y = 24

4(6) -5(0) = 24

24 + 0 = 24

24 = 24

Therefore, (6, 0) is a possible solution to the equation.

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Answer:

BELOW

Step-by-step explanation:

The equation ( you need to commit to memory) is:

FV = PV ( 1+i)^n      FV = future value    PV = present value(270)

                                     i = decimal interest per PERIOD = .15

                                       n = # of periods = 3  (it is an ANNUAL Period)

FV = 270 ( 1 + .15)^3 = 410.63 dollars

Answer:

$410.64

Step-by-step explanation:

start with the compound interest formula

plug in p=270 , r=0.15 (divide 15 by 100 to get 0.15), n=1, and t=3

divide 0.15 by 1 to get 0.15

multiply the exponents 1 and 3 to get 3

add 1 and 0.15 to the 3 th power to get 1.520875

multiply 270 and 1.520875 to get 410.63625

so if you invest $270 at an interest rate 15%, which is compounded 1 times a year for 3 years, the return is about $410.64 (which is rounded to the nearest cent)

Then you'll have $410.64 in 3 years.

For the given condition of choosing president and treasurer from the 10 board members on the Community Arts Council , the total number of outcomes president and treasurer can be chosen as

Combination ; 45 ways.

As given in the question,

Total number of board members in the Community Arts Council = 10

Number of people to be chosen from Community Arts Council (president and treasurer) = 2

Total number of ways to choose a president and treasurer is calculated using combination of selecting 2 people is equal to

= ¹⁰C₂

= ( 10 )! / ( 2! ) ( 10 - 2 )!

= ( 10 × 9 × 8! ) / ( 2 × 1 ) ( 8! )

= 90 / 2

= 45

Therefore, for the given condition of choosing president and treasurer from the 10 board members on the Community Arts Council , the total number of outcomes president and treasurer can be chosen as

Combination ; 45 ways.

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The equation of a line that is perpendicular to -9x = 15 - 3y is y = -1/3(x) + c.

Given:

-9x = 15 - 3y

3y = 15+9x

divide by 3 on both sides

3y/3 = 15/3 + 9x/3

y = 3x + 5

m = 3

Perpendicular slope m1 = -1/m

= -1/3

substitute m value in y = m1x +c

y = -1/3(x) + c.

Therefore the equation of a line that is perpendicular to -9x = 15 - 3y is y = -1/3(x) + c.

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Answer:

16

Step-by-step explanation:

multiply sides

The estimate of the number of transistors per IC in 2016 is of:

16,777,216,000

Using Moore's Law, the prediction for the number of transistors per IC to be in 2040 is of:

6.87 x 10¹³

Moore's Law states that the number of transistors per IC is expected to double every two years.

Hence the amount of transistors in t years after 1972 is given by the following exponential function:

[tex]A(t) = 4000(2)^{\frac{t}{2}}[/tex]

The number of years between 2016 and 1972 is given as follows:

2016 - 1972 = 44.

Hence the estimate for the number of transistors per IC in 2016 is of:

[tex]A(44) = 4000(2)^{\frac{44}{2}}[/tex]

A(44) = 16,777,216,000

The number of years between 2040 and 1972 is given as follows:

2040 - 1972 = 68.

Hence the estimate is obtained as follows:

[tex]A(68) = 4000(2)^{\frac{68}{2}}[/tex]

A(68) = 6.87 x 10¹³.

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The probability that the hat was blue or was from Manufacturer B is 0.8677.

The P[tex](red)^{c}[/tex] is 0.6985.

The P(manufacturer B and Red) is 0.1640.

The P(Manufacturer B or Red) is 0.8456.

Probability is used to determine the odds that a random event would happen. The odds that the random event happens range from 0 to 1.

The probability that the hat was blue or was from Manufacturer B = (number of blue hats / total number of hats) + (number of hats from manufacturer B / total number of hats)

The probability that the hat was blue or was from Manufacturer B = (44 / 136) + (74 / 136) = 118/136 = 0.8677

The P[tex](red)^{c}[/tex] = complement of red = hats that are not red = (number of black hats + number of blue hats) / total number of hats

The P[tex](red)^{c}[/tex] = (51 + 44) / 136

The P[tex](red)^{c}[/tex] = 95 / 136

The P[tex](red)^{c}[/tex] = 0.6985

The P(manufacturer B and Red) = (number of hats produced by manufacturer B / total number of hats) x (number of red hats / total number of hats)

(74 / 136) x (41 / 136) = 0.1640

The P(Manufacturer B or Red) =  (number of hats produced by manufacturer B / total number of hats) + (number of red hats / total number of hats)

(74 / 136) + (41 / 136) = 115 / 136 = 0.8456

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Answer:

If you divide 600/ 45 mins you get the kilometers per minute which is 13.33. Then you multiply 13.33 times 30 mins and you get 399.9 or 400 kilometers

Step-by-step explanation:

If the two cyclists are 82 miles apart after 2 hours, The rate of each cyclist is: The slower cyclist's speed is 17 mph and the faster cyclist's speed is 24 mph.

Let x mph = speed of the slower cyclist = (x +7) mph

Let 2x miles represent the slower cyclist has traveled

2(x + 7) = 2x + 14 miles

Hence,

2x + (2x + 14) = 82

4x = 68

Divide both side by 4x

x = 68/4

x= 17 mph (slower)

So,

(x +7) mph

= 17 + 7

= 24 mph (fastest)

Therefore the speed is 17 mph and 24 mph.

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According to the concept of inequality, the interval notation is 0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85 based on these range the second and third car seats are suitable.

Inequality:

Inequality refers the non equal relation of the sets.

Given,

A family is comparing different car seats. One car seat is designed for a child up to and including 25 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 25 lb and 85 lb, inclusive. Model those ranges with compound inequalities.

Here we need to find in which car seats are appropriate for a 35-lb child

In this question, they provided that, there are three car seats are designed as follows:

First, on is the car seat made for children upto 30lb.

Second one is the seat for children between 15lbs and 40lbs and

And the third one is the seat designed for a child between 30 lb and 85 lb

Here we know that, the seat designed for a child upto and including 30 lb would not be suitable for 35 lb child. Because 35lb is more than the 30 lb.

So, now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 35lb.

Therefore, the interval notation is written as,

=> 0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

So, the  second and third car seats are suitable.

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Answer:

175760000

Step-by-step explanation:

There are 10 possibilities for each number and 26 possibilities for each letter.

Using the multiplication principle, the answer is [tex](10)(26^3)(10^3)=175760000[/tex]

For an atom to be considered as such it needs to be composed of subtatomic particle (neutrons, electrons, protons), an molecule includes two or more atoms, an element has defined properties and a compound includes two or more element.

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The inequality to determine the number of days, d, it will take Katie to collect over 100 seashells is 34 + 12d > 100.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of days be represented by d.

In this case, Katie already has 34 seashells in her collection and each day, she finds 12 more seashells on the beach.

The expression will be:

34 + 12d > 100

Collect like terms

12d > 100 - 34

12d > 66

Divide

d > 66/12

d > 5.5

d > 6

The number of days is 6 days.

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Answer:

Step-by-step explanation:

Ok:

Flour:

2 1/4 cups/1/4c=

9 cups needed

Sugar:

1 7/4/1/4=

11 cups needed

Cocoa:

1 1/2/1/4=

6 cups needed

Oil:

1/2/ 1/4=

2 cups needed

Heavy Cream:

3 2/3/ 1/3=

11 cups needed

Butter:

1/1/3=

3 cups needed

Powdered Sugar:

5 1/3/1/3=

16 cups needed

Cocoa:

1/3/1/3( Sry if I read the 3 wrong because its blurry tell me and I will fix it!)=

1 cup needed

Answer:

y = -14x + 61

Step-by-step explanation:

You need the slope and the y-intercept to write the equation.  They give us the slope.  We will use the point given (4,5) to find the y intercept.  A point is given in the form (x,y)

slope (m) = -14

y = 5   Given from the point (4,5)

x = 4  Given from the point (4,5)

y = mx + b  Plug in what we know

5 = -14(4) + b

5 = -56 + b  Add 56 to both sides of the equation

61 = b

y = -14x + 61

Based on the z-score value, Latisha earned a higher IQ score.

In order to determine the person who earned a higher IQ score, we would have to calculate the z-score for the two IQ tests that Felix and Latisha took.

Mathematically, the z-score of a given sample score can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

For Felix, we have the following:

Z-score = (130 - 105)/10

Z-score = 25/10

Z-score = 2.5.

For Latisha, we have the following:

Z-score = (120 - 95)/5

Z-score = 25/5

Z-score = 5.0.

Therefore, Latisha had the higher score because she has a higher z-score than Felix.

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