Unit 3: Relations and Functions
Homework 1: Relations,domain,range,and functions

The equation of the line y = - (13 / 5) · x - 56 / 5 passes through the points (x₁, y₁) = (- 7, 7) and (x₂, y₂) = (- 2, - 6).

In this question we must derive the equation for a line that passes through two points on Cartesian plane. This can be done by means of the following two formulas:

Secant line formula

m = Δy / Δx

Equation of the line in slope-intercept form

y = m · x + b

Where:

First, write the given points:

(x₁, y₁) = (- 7, 7), (x₂, y₂) = (- 2, - 6)

Second, determine the slope of the line:

m = (- 6 - 7) / [- 2 - (- 7)]

m = - 13 / 5

Third, calculate the intercept of the equation of the line:

b = y - m · x

b = - 6 - (- 13 / 5) · (- 2)

b = - 6 - 26 / 5

b = - 30 / 5 - 26 / 5

b = - 56 / 5

Fourth, write the resulting equation of the line:

y = - (13 / 5) · x - 56 / 5

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Answer:

$1

Step-by-step explanation:

1 quarter: 25 cents

3 nickels: 15 cents

6 dimes: 60 cents

25+15+60= 100 cents, and 100 cents make up exactly 1 dollar.

The simplified expression of 3y + 6x - 2x - 2y is y + 4x.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations like addition and subtraction.

To simplify an expression means to write an equivalent expression which contains no similar terms or rewriting the same algebraic expression with no like terms.

Therefore, let's simplify the expression with no like terms as follows;

3y + 6x - 2x - 2y

combine like terms

3y - 2y + 6x - 2x

Therefore, the simplified expression is y + 4x

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Answer:

P≈28.28cm  = 28 cm

Step-by-step explanation:

Using the formulas

P=4a

d=√2a

Solving forP

P=2 √2d=2·√2·10≈28.28427cm

Answer:

x = [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

- 4x + 3 = 2(x - 1) ← distribute parenthesis by 2

- 4x + 3 = 2x - 2 ( subtract 2x from both sides )

- 6x + 3 = - 2 ( subtract 3 from both sides )

- 6x = - 5 ( divide both sides by - 6 )

x = [tex]\frac{-5}{-6}[/tex] = [tex]\frac{5}{6}[/tex]

Answer: B.

Step-by-step explanation:

x+2y≤4

3x-y≥2

The likelihood that the next 20 marbles picked will be yellow marbles is 9/20.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The probability that of the next 20 marbles selected it is expect to be yellow marbles,

=9/20

The probability that of the next 20 marbles selected it is expect to be yellow marbles will be 9/20.

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Answer:

the answer is 10

Step-by-step explanation:

ixl says its ten

Using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.

A percentage is a relative figure that has the ability to represent 1/100th of any quantity.

Since 1% denotes one percent, 100 percent and 200 percent indicate the full amount and double the quantity, respectively.

By multiplying by 100 and inserting the "percentage sign"%, a ratio and fraction can be transformed into a percentage.

So, Luce is single and makes $763 twice weekly.

She does not request any compensation from federal withholding.

The value of this amount ranges from $760 to $780.

If we look at the table in the issue, the federal tax for this slab is $86.

Federal taxes now make up 19% of all state taxes.

Hence, the $86 in federal tax at a rate of 19% is:

Tax = 86 * 19/100

Tax = 16.34

Therefore, using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.

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Correct question:

Use the tax table to help answer the following question.

A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.

Luce is single and makes $763 biweekly. She claims no federal withholding allowances. If the state tax is 19% of the federal tax, how much in state tax does Luce contribute?

a. $12.92

b. $15.13

c. $15.77

d. $16.34

A box of a dozen donuts, the probability that you randomly choose a chocolate donut from the box is 1/3 ....

Probability is the study of occurrence of chance of a particular result. It is calculated by ratio of favourable outcomes and the total possible outcomes.

We have box of a dozen donuts contains,

The number of glazed donuts in box = 5

The number of blueberry donuts in box = 3

The number of chocolate donuts in box = 4

So, the total number of donuts = 12

We have to calculate probability that you randomly choose a chocolate donut from the box, say P(X) .

That is one donut is selected randomly from box.

P(X) = Number of favourable cases/ Total number of possible outcomes

= 4/12 = 1/3

Thus, the required probability is 1/3.

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Answer:

Step-by-step explanation:

You want to know the measure of angle 1 given that angle 2 is 14° more and their total is 80°.

The angle sum theorem tells you the whole is equal to the sum of the parts.

  ∠1 +∠2 = ∠ABD

Using the given values, we have ...

  ∠1 +(∠1 +14°) = 80°

  2×∠1 = 66° . . . . . . . . . subtract 14°

  ∠1 = 33° . . . . . . . . divide by 2

  ∠2 = 33° +14°

  ∠2 = 47°

The seventh term in the geometric sequence is 2097152.

A geometric progression, also known as a geometric sequence in mathematics, is a chain of non-zero numbers where each term after the first is created by multiplying the previous term by a fixed, non-zero amount known as the common ratio. A geometric progression, also known as a geometric sequence in mathematics, is a chain of non-zero numbers where each term after the first is created by multiplying the previous term by a fixed, non-zero amount known as the common ratio. The sequence 2, 6, 18, 54, etc. is one example of a geometric progression with a common ratio of three. In a manner similar to that, a geometric series with a common ratio of 1/2 is composed of 10, 5, 2.5, 1.25, etc.

Given,

The geometric sequence is 8, 64, 512, 4096, .......

It follows the sequence like 2³, 4³, 8³, 16³, 32³, 64³, 128³

The seventh term in the geometric sequence is 128³=2097152

Therefore, the seventh term in the geometric sequence is 2097152.

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Answer:

x < -3

Step-by-step explanation:

15 < -5x

15/-5 > -5x/-5

-3 > x

Move the variable to the left and flip the inequality

x < -3

If the probability that a hurricane will make landfall in Florida is 49%, then the probability that a hurricane will not make landfall in Florida is 51%

The probability that a hurricane will make landfall in Florida = 49%

The probability is the ratio of number of favorable outcomes to the total number of outcomes

The equation of probability will be

Probability = Number of favorable outcomes / Total number of outcomes

Given that

The probability that a hurricane will make landfall in Florida  = 49%

The probability that a hurricane will not make landfall in Florida = 1 - The probability that a hurricane will make landfall in Florida

= 1 - 0.49

= 0.51

= 51%

Therefore, the probability that a hurricane will not make landfall in Florida is 51%

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Answer: 54.5

Step-by-step explanation: 54.5

Answer:

śiŕe ťhe śeçondè çolumm y has ťhe èntieŝ 2 2 2 2

Step-by-step explanation:

ĥopè ťis ĥeĺpś

The rate of interest in one account whose investment is $2300 will be 3.21%.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.

Let 'x' be the interest. Then the equation is given as,

(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130

Simplify the equation, then we have

23x + 56 = 130

23x = 74

x = 3.21%

The pace of revenue in one record whose speculation is $2300 will be 3.21%.

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The inverse function is given by f⁻¹(x) = 1.06x.  2 euros is equivalent to 2.12 U.S. dollars. 4 euros is equivalent to 4.24 U.S. dollars

Given that: the two different currencies is modeled by a linear function f(x) = x/1.06

where, x = an amount in U.S. dollars and f(x) = the equivalent amount in euros

To find the inverse function f⁻¹(x). Let y = f(x):

y = x/1.06

x = 1.06y

Since x = f⁻¹(y) = 1.06y

Thus, f⁻¹(x) = 1.06x

Note: f⁻¹(x) will help you convert from euros to dollar

2 euros to dollars will be:

f⁻¹(x) = 1.06x

f⁻¹(2) = 1.06(2) = 2.12

Thus, 2 euros is equivalent to 2.12 U.S. dollars

4 euros to dollars will be:

f⁻¹(x) = 1.06x

f⁻¹(4) = 1.06(4) = 4.24

Thus, 4 euros is equivalent to 4.24U.S. dollars

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first 2;

a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32

36 - 22 = 14/2 = 7

32 - 16 = 16/2 = 8

7<8

the table has a greater rate of change

y intercept

equation; 8

table; 0

8> 0

the equation has a greater y intercept

Answer:

2

Step-by-step explanation:

-2 and -4 are less than 0

2 is greater than

If you write down in descending order ===> 2, -2 , -4

Answer:

Below

Step-by-step explanation:

See image:

The reasonable domain for the range: 68,71,74,77,80 is { 1,2,3,4,5 } .

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.  

Given:

range: 68,71,74,77,80

Domain:1,2,3,4,5

Here, the situation is not given.

So, the reasonable domain is { 1,2,3,4,5 }

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The chances that the revenue on the first show will exceed $800 when mean revenue is $336.25 and standard deviation is $38.16 is essentially zero. i.e. 0

A normal distribution is a type of continuous probability distribution in which the majority of data points cluster in the middle of the range, while the remainder taper off symmetrically toward either extreme. The mean of the distribution is also known as the middle of the range.

The normal distribution is primarily used to calculate the likelihood of an observation in a distribution falling above or below a given value.

Given,

Mean, [tex]\mu[/tex] = 336.25

variance, [tex]\sigma^2[/tex]= 1456

then,

standard deviation, [tex]\sigma = \sqrt{1456}[/tex] = 38.16

To determine the chances that the revenue on the first show will exceed 800 is1:

[tex]1-p(z=\frac{x-\mu}{\sigma})\\\\=1-p(z=\frac{800-336.25}{38.16})\\\\=1-p(z=\frac{436.75}{38.16})\\\\=1-p(z=12.15)\\\\=1-1=0[/tex]

Hence, there is no chance that the revenue will exceed $800 on the first show.

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Using the binomial distribution, it is found that there is a 0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.

For each chicken, there are only two possible outcomes, either they are contaminated, or they are not. The chickens are independently selected, hence, the binomial distribution is used.

What is the binomial probability distribution formula?

The formula is:

P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ

Cₙ,ₓ = n!/x!(n-x)!

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

About 30% of frozen chickens are contaminated, hence p=0.3.

Chickens are delivered to grocery stores in crates of 24, hence n=24

The probability that a certain crate has more than 4 contaminated chickens is:

P(X>4)=1-P(X≤4)

In which:

P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

Then

P(X=x) =  Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ

P(X=0) = C₂₄,₀.(0.3)⁰.(0.7)²⁴ = 0.0002

P(X=1) = C₂₄,₁.(0.3)¹.(0.7)²³ = 0.0020

P(X=2) = C₂₄,₂.(0.3)².(0.7)²² = 0.0097

P(X=3) = C₂₄,₃.(0.3)³.(0.7)²¹ = 0.0305

P(X=4) = C₂₄,₄.(0.3)⁴.(0.7)²° = 0.0687

Hence

P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

= 0.0002+0.0020+0.0097+0.0305+0.0687

= 0.1111

0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.

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Answer: grace has the most money

Step-by-step explanation:

Because

Grace has 2 quarters = 50 cents

Jen has 4 dimes and 1 nickel = 45 cents

Keesha has 3 dimes and 3 nickels = 33 cents

Terry has 1 quarter and 1 dime = 26 cents

so as you can see grace has the most money

The distance travelled by car in 90 minutes will be 1.5x miles. The correct option is B.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that If a car travels at an average speed of x miles per hour. The distance travelled by car in 90 minutes will be calculated as,

x miles ⇒ 1 hours

x miles ⇒ 60 minutes

1 minute ⇒ x / 60 miles

90 minutes ⇒ ( 90x) / 60

90 minues ⇒ 1.5x miles

The missing options are given below.

A. 1.5x miles

B. 3x miles

C. 2x miles

D. 4x miles

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Hello,

I hope you and your family are doing well!

Since AB || DC and AD = BC, trapezoid ABCD is a parallelogram, which means that its opposite sides are parallel and congruent. Therefore, angle A is congruent to angle C and angle B is congruent to angle D.

Since mA = 4x+20 and m/C= 3x - 15, we know that mA + mC = 4x+20 + 3x - 15 = 7x + 5.

Since angles A and C are congruent, we can set their measures equal to each other:

mA = mC

4x+20 = 3x - 15

Solving this equation for x gives us x = 5. Substituting this value back into the equation mA + mC = 7x + 5 gives us:

mA + mC = 7 * 5 + 5 = 35

The answer is 35 (Option 2)

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Happy Holidays & New Year!

The solution is, the value of m is is 35 (Option 2).

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

hee, we have,

Since AB || DC and AD = BC, trapezoid ABCD is a parallelogram, which means that its opposite sides are parallel and congruent. Therefore, angle A is congruent to angle C and angle B is congruent to angle D.

Since mA = 4x+20 and m/C= 3x - 15, we know that mA + mC = 4x+20 + 3x - 15 = 7x + 5.

Since angles A and C are congruent, we can set their measures equal to each other:

mA = mC

4x+20 = 3x - 15

Solving this equation for x gives us x = 5.

Substituting this value back into the equation mA + mC = 7x + 5 gives us:

mA + mC = 7 * 5 + 5 = 35

The answer is 35 (Option 2)

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Answer:

code : fasmej ??

Step-by-step explanation:

1. F

2. A

3. S

4. M

5. E

6.J