No, a **function** whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree is not a **one-to-one function**.

A **one-to-one function **is also referred to as an injective **function** and it can be defined as special type of **function** in which every element of the range is mapped to exactly a single element of its domain. This ultimately implies that, the output values (y-values) of a **one-to-one function **never repeat themselves.

Additionally, a **one-to-one function** maps distinct elements of its domain (y-values) to distinct elements of the range (x-values) and as such, it connotes the mapping of two (2) sets.

In this context, we can reasonably and logically deduce that this **function **is not a **one-to-one function **because it fails the horizontal line test as there could be the same temperature at different times of the day.

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HELP Please!!!

Bridget worked on her Math homework for 1 ½ hours. Then she worked on her Social Studies homework for ¼ hour. How many hours total did she work on her homework?

Be sure to show all of your work and steps.

**Answer: 1 3/4**

**1/4= 15 minutes**

**1/2 = 30 minutes**

**add 1/2 to 1/4 and you get 3/4 because 1/2 is equal to 2/4 if you add the 1/4 to it**

**heres the actual math:**

**1/2 = 2/4**

**2/4 + 1/4 = 3/4**

**slap that one in front of it so its 1 3/4 and therea your answer **

A woman earned wages of $34,600, received $1500 in interest from a savings account, and contributed $2700 to a tax-deferred retirement plan. She was entitled to a personal

exemption of $2900 and had deductions totaling $5090. Find her gross income, adjusted gross income, and taxable income.

If She was entitled to a personal exemption of $2900 and had deductions totaling $5090. her **gross **income is $36,100, adjusted gross income is $33,400 , and **taxable **income is $25,410.

**Gross **Income:

Gross Income= Wages + Interest received

Gross Income= 34,600 + $1500

Gross Income= $36,100

**Adjusted **Gross Income:

Adjusted Gross Income = Income - Tax Def Contribution

Adjusted Gross Income = $36,100- $2,700

Adjusted Gross Income = $33,400

**Taxable** Income :

Taxable Income = AGI - Deductions - Personal exemption

Taxable Income= $33,400- $5,090 - $2,900

Taxable Income= $25,410

Therefore her **gross **income is $36,100.

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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > -2 x - 7I NEED THE CORDINATES

**Given:**

There are given that the set of inequality is:

[tex]\begin{gathered} y>x+2 \\ y>-2x-7 \end{gathered}[/tex]**Explanation:**

From the given system of inequality, we need to draw the graph and find the set of points, where both of the graphs will intersect.

Now,

The graph of the given system of inequality is shown below:

**Final answer:**

Hence, **the set of the point from the given system of inequality is shown below:**

Find the slope, x-intercept, and y-intercept for the line 10x-7y + 7 = 0. The slope is The I-intercept is h The y-intercept is Note: Your answers must be decimals. Submit Question Jump to Answer

slope=1.43

y-intercept=1

x-intercept=-1.43

**Explanation**

**Step 1**

get the slope intercept form of the equation

[tex]y=mx+b\text{ (slope intercept equation)}[/tex]where

m is the slope and b is the y-intercept

to do this, isolate y

[tex]\begin{gathered} 10x-7y+7=0 \\ \text{subtract 10 x in both sides} \\ 10x-7y+7-10x=0-10x \\ -7y+7=-10x \\ \text{subtract 7 in both sides} \\ -7y+7-7=-10x-7 \\ -7y=-10x-7 \\ divide\text{ both sides by -7} \\ \frac{-7y}{-7}=\frac{-10x}{-7}-\frac{7}{-7} \\ y=\frac{10x}{7}+1 \end{gathered}[/tex]so,

[tex]\begin{gathered} \text{slope}=\frac{10}{7} \\ y-\text{intercept}=1 \end{gathered}[/tex]**Step 2**

to find the x-intercept replace the y value with zero in the equation

[tex]\begin{gathered} y=\frac{10x}{7}+1 \\ 0=\frac{10x}{7}+1 \\ \text{subtract 1in both sides} \\ 0-1=\frac{10x}{7}+1-1 \\ \frac{10x}{7}=-1 \\ \text{Multiply both sides by 7/10} \\ \frac{10x}{7}\cdot\frac{7}{10}=-1\cdot\frac{7}{10} \\ x=-\frac{7}{10} \end{gathered}[/tex]so, the x intercept is

[tex]-\frac{7}{10}[/tex]I hope this helps you

A Christmas tree is supported by a wire that is 3 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 21 meters shorter than the height of the tree. What is the height of the tree?

The **height **of the Christmas **tree **is 12 meters

Represent the **height **of the **tree **with h

So, we have the following parameters

Tree height = hBaseline = h - 21Anchor = h + 3The figure that illustrates the above parameters is added as an attachment

From the figure, we have the following equation by **Pythagoras theorem**

(h + 3)² = h² + (h - 21)²

Expand the exponents

h² + 6h + 9 = h² + h² - 42h + 441

Evaluate the like terms

6h + 9 = h² - 42h + 441

So, we have

h² - 48h + 432 = 0

Expand

h² - 36h - 12h + 432 = 0

Factorize the equation

(h - 36)(h - 12) = 0

Solve for h

h = 36 and h = 12

When h = 36, the **baseline **will be negative

So, we make use of h = 12

Hence, the **tree **has a **height **of 12 meters

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In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to

a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?

The probability that a female will be born using this technique is approximately

(Type an integer or decimal rounded to three decimal places as needed.)

Does the technique appear effective in improving the likelihood of having a female baby?

O No

O Yes

The **probability** of having female baby is 0.95

**What is probability?**

**Probability** is a discipline of mathematics that deals with statistical models of how probable an event is to exist or how likely a statement is to be true. The **probability** of an occurrence is a value between 0 and 1 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the **probability** of "tails," and because no other outcomes are possible, the **probability** of either "heads" or "tails" is 1/2.

The **probability** of having female baby is = 284/(284 + 15) = 0.95

** **

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Change the function, y=3(0.5)^x,to a function with base e

**Answer:**

**y = 3(e)^(-0.69x)**

**Explanation:**

Taking into account the following property

[tex]a=e^{\ln a}[/tex]We can replace (0.5)^x by

[tex]\begin{gathered} 0.5^x=e^{\ln \text{ (0.5\textasciicircum{}x)}} \\ 0.5^x=e^{x\ln (0.5)} \end{gathered}[/tex]So, now we can rewrite the function as

[tex]\begin{gathered} y=3e^{x\ln (0.5)} \\ y=3e^{x(-0.69)} \\ y=3e^{-0.69x} \end{gathered}[/tex]Therefore, the answer is

y = 3(e)^(-0.69x)

**Answer:**

y=3e^(ln0.5)x

**Step-by-step explanation:**

if your 1952 what year will you be 26?

**Answer:**

16 January 1952, Wednesday, 70 Years, 8 Months, 26 Days or 848 months, or 3691 weeks, or 25837 days, or 37205280 minutes, or 2232316800 seconds.

**Step-by-step explanation:**

**Answer:**

**Step-by-step explanation:**

answer:1978

Simplify the following expression by expanding and collecting like terms.-(7x + 6) + 3(-5x – 3)Give your answer in the form ax + b.Provide your answer below:

**ANSWER**:

**STEP-BY-STEP EXPLANATION:**

We have the following expression:

[tex]-\mleft(7x+6\mright)+3\mleft(-5x-3\mright)[/tex]We solve and reduce like terms, just like this:

[tex]\begin{gathered} -7x-6-15x-9 \\ (-7x-15x)+(-6-9) \\ (-22x)+(-15)=-22x-15 \end{gathered}[/tex]Please Help With This.

The angle** m∠FCD is 56°**

Here the line **CF is an angle bisector of ∠GCD.**

By this we have,

**∠GCF = ∠FCD**

It is given that

∠GCF = ∠GCB - 12°

Let ∠GCB be x.

∠GCF = x - 12° = ∠FCD

**BCD is a straight line** which form 180°.

∠BCG + ∠GCF + ∠FCD = 180°

x + x - 12° + x - 12° = 180°

3x = 204°

x = 68°

∠FCD = x - 12°

= 68° - 12°

= 56°

Therefore **m ∠FCD = 56°.**

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What's the radius of 5?

The formula for radius is

radius = diameter/2

If diameter = 5, then

radius = 5/2

radius = 2.5

What is the unit rate of the graph below make sure you use answer include unit three point￼

**Answer:**

have you heard of the genger bread man

**Step-by-step explanation:**

The perimeter of a triangle is 38 feet. One side of the triangle is one foot longer than the second side. The third side is four feet longer than the second side. Find the lengths of all three sides (in feet). (Enter your answers as a comma-separated list.)

The length of the three sides of the **triangle** are 11 feet, 12 feet and 15 feet.

A **triangle** is a polygon with three sides.

The perimeter of a triangle is 38 feet.

The perimeter of the **triangle** is the sum of the whole three sides.

One side of the triangle is one foot longer than the second side.

let

the second side = x

longer side = x + 1

The third side is four feet longer than the second side.

Hence,

Third side = 4 + x

Therefore,

38 = x + x + 1 + x + 4

38 = 3x + 5

3x = 38 - 5

3x = 33

x = 33 / 3

x = 11

Therefore, the sides of the** triangle **are 11 ft, 12 feet and 15 ft.

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Given the following sequences: I. 2,4,6,8,10... II.2,4,8,16,32... III. a,a + 2, a + 4, a + 6, a +8... Which ones are arithmetic sequences?

**ANSWER**

The arithmetic sequences are: **I **and **iii**

**EXPLANATION**

The formula for the nth term of an arithmetic sequence is:

[tex]a_n=a_1+d(n-1)[/tex]where a1 is the first term of the sequence and d is the common difference.

For the first sequence **I**. 2, 4, 6, 8, 10... we can find the common difference by subtracting the first term from the second:

So the nth term of this sequence is:

[tex]a_n=2+2(n-1)[/tex]Each term of this sequence follows this rule. Therefore this is an arithmetic sequence.

For the second sequence **II**. 2, 4, 8, 16, 32... there's no common difference because between the first and second term there's a difference of 2, between the second and third there's a difference of 4, and this increases as we move through the sequence. Therefore this is **not** an arithmetic sequence.

For the third one, **III**. a, a+2, a+4, a+6, a+8... we can see that there is a common difference:

The rule for the nth term is:

[tex]a_n=a+2(n-1)[/tex]Let's find the first 5 terms:

[tex]\begin{gathered} a_1=a+2(1-1)=a \\ a_2=a+2(2-1)=a+2 \\ a_3=a+2(3-1)=a+4 \\ a_4=a+2(4-1)=a+6 \\ a_5=a+2(5-1)=a+8 \end{gathered}[/tex]This shows that each term follows the same rule. Therefore this is an arithmetic sequence.

What is the value of the missing angle

**Answer: 105**

**Step-by-step explanation:**

Angles in a triangle add up to 180 degrees always, you already have two angles. Subtract those two angles from 180 then you have 75. A straight line always equals 180, and since we just found one angle on that line which is 75, just subtract 75 from 180 to get the answer.

Give a brief history about TRIANGLE NUMBERS, including Mathematicians that contributed for its development.

Brief history of triangle numbers

**What is Triangle Number?**

An equilateral **triangle**-shaped group of objects is counted using a **triangular number **or **triangle number**. Square and cube numbers are two further examples of figurate numbers, which also include **triangle numbers**.

Students are typically introduced to **triangular numbers **through the account of Carl Gauss, a well-known mathematician who used the concept of the **triangle number **formula to aid him with summing consecutive integers as a student. This tale and its applications in many situations are discussed in the article Clever Carl.

**Triangular numbers **were created by the Pythagoreans, who discovered connections between geometric forms and numbers, giving rise to **triangular**, square, pentagonal, and other numbers.

After four or five terms, students may recognize that the answer can be discovered by adding consecutive terms, according to our research. As an illustration, you may use the formulas 1+2+3+4+5 or 10 (the preceding term) + 5 to determine the fifth term. However, when students attempt to transition from this to the general formula for **triangle numbers **of

n(n+1)/2

Drawing **triangle numbers **is an exercise that could be helpful in establishing a connection between these two concepts.

The nth term and substitution into algebraic expressions can then be discussed using this formula. Sequences, notably quadratic sequences, can also be discussed.

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use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph (without drawing the graph) a graph with 4 vertices, each of 2 degree 2

[tex]\begin{gathered} \text{Handshaking theorem} \\ Sum\text{ of degre}e\text{ of all the vertices=2}\times Number\text{ of vertices} \\ So,\text{ } \\ n\times2=2\times4 \\ n=4(nu\text{mber of edge)} \end{gathered}[/tex]

The square of a negative number

is sixteen more than six times the

negative number. Find the number. The sum of two numbers is

twenty three. And The product of the

two numbers is one hundred

twenty. Find the two numbers.Help me. From: Jessie

The** numbers **are**:**

1.** **The value of **x = 5**

2.** **The value of **x = 15 or 8** and **y = 8 or 15**

**What is Square?**

The word** Square **means a **number **multiplied by itself.

The above answers were gotten in the following way:

1. Let the unknown **negative number** be x

The **square** of the **negative number**: x² is

Sixteen more than six times of negative x: 6x+16

It is written as: (x)²=6x+16

Equating to zero, we have:

x²-6x-16=0

Factorizing, we have:

x²-8x+2x-16=0

x(x-8)+2(x-8)=0

x+2=0 and x-8=0

x=-2 and 8

Since the number is negative, x = -2

Therefore, the value of the **negative number** is -2

2. Given:

Sum of **two numbers** = 23

Product of** two numbers** = 120

Calculation:

Let the **two** **numbers** be x and y

x+y=23...............equation 1

xy=120..................equation 2

From equation 1, x=23-y

Substitute the value of x in equation 2**, **we have:

(23-y)y=120

Opening the brackets, we have:

23y-y²=120

Rearranging the equation, we have:

-y²+23y=120

Equating to zero, we have:

-y²+23y-120=0

Multiplying both sides by (-1), we have:

y²-23y+120 = 0

Factorizing, we have:

y²-15y-8y+120=0

y(y-15)-8(y-15)=0

(y-8)(y-15)=0

y=8 or 15

Substituting the values of y in any of the equation. Choosing equation 1, we have:

From Equation 1: x+y=23

When y=8,

x+8=23

x=23-8

x=15

When y=15

x+15=23

x=23-15

x=8

Therefore the values of the **two numbers** are 15 and 8

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3х-7-(-2х) +9 simplify

[tex]3x-7-(-2x)+9[/tex][tex]\begin{gathered} 3x-7+2x+9 \\ (3+2)x+(-7+9) \\ 5x+2 \end{gathered}[/tex]

A population of a certain city increases exponentially at a rate of 6.5%. Initially, it is 1.50 million. After how many years will the population reach 2.31 million?6.5466.643 6.1236.142

**Given that **

The population of a certain city is 1.50 million initially and it gets increased by 6.5% exponentially. And we have to find the number of years in which the population becomes 2.31 million.

**Explanation **-

The formula for the exponential growth is given as

[tex]\begin{gathered} f(x)=a(1+r)^x \\ where\text{ f\lparen x\rparen is the final amount, a = initial amount, r = rate and x = time period} \end{gathered}[/tex]Here we have f(x) = 2.31 million, a = 1.50 million , r = 6.5% and x = ?

So let the time be t.

Then, on substituting the values we have

3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.

3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.

________________________________

# of Chocolates Price Ratio (Price per chocloate)

Store A 36 pack box 54 54/ 36 = 3/2 = 1.5

Sotre B 6-pack boxes 12 12/ 6 = 2

_____________________________

Store A 1.5

______________________________

Answer

Store A offers a better deal

What is the net price of merchandise listing for $5,900 less a trade discount rate of 45%?

A percentage is a number or ratio that represents a fraction of 100.

If there is a trade discount of 45% on the price of the merchandise of $5900, the **net** **price** of the **merchandise** is $3245.

A percentage is a number or ratio that represents a fraction of 100.

We have,

**Merchandise** price = $5,900

**Discount** rate = 45%

45% = 45/100 = 9/20

The **net** **price** of the **merchandise**:

= 5900 - (45% of 5900)

= 5900 - 9/20 x 5900

= 5900 - 9 x 295

= 5900 - 2655

= 3245

Thus,

If there is a trade discount of 45% on the price of the merchandise of $5900, the **net** **price** of the **merchandise** is $3245.

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In a recent year, 31.4% of all registered doctors were female. If there were 47,300 female registered doctors that year, what was the total number of registered doctors?

**Proportionately**, the total number of registered doctors, based on the **ratio** of female doctors, is 150,637.

**Proportion** refers to the quantity relationship of a variable contained in another.

Using **proportion**, two values are equated to each other.

For instance, we equate the **percentage** of registered female doctors to the number of registered female doctors.

**Proportions**, like **ratios**, are stated as fractions, decimals, or percentages because they depict the portion of a variable in another.

The ratio of registered female doctors = 31.4%

The number of registered female doctors = 47,300

31.4% = 47,300

100% = 47,300/31.4% x 100

The total number of registered doctors = 150,637 (47,300/31.4%)

Thus, the total number of registered doctors is 150,637, given that 47,300 female registered doctors **proportionately** represent 31.4% of the population.

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60x-30/5=18. please help meeeeee. 10 pts worth.

60x - 30/5 = 18

60x - 6 = 18

60x = 24

x = 0.4

60x - 6 = 18

60x = 24

x = 0.4

James spins a basketball on his finger and then passes the ball to his friend.

a. What type of transformation is used when James spins the basketball on

his finger?

b. What type of transformation is used to pass the basketball?

The types of** transformations **that occur as a result of the motion on the ball are;

A) Rotation

B) Translation

What is the type of transformation?**Transformation** is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.

**Translation** is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.

**Reflection** is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.

**Rotation **is a method of transformation that involves turning a given figure at an angle about a reference point.

**Dilation** is a method of transformation whereby the length of the sides of the figure is either increased or decreased.

A) When James spins a basketball on his finger, it is clear that this transformation is rotation because it involves turning the ball at an angle about a given point.

B) When James passes the basketball, the transformation would be translation because it involves moving the ball from one point to another without changing the dimension of the ball.

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Here is the probability model for the blood type of a randomly chosen person in the United States:Blood Type O А B ABProbability 0.14 0.32 0.01 ?(a) This probability model isA. discrete.B. continuousC. equally likelyD. None of the above.(b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that arandomly chosen American can donate blood to Maria?A. 0.01B. 0.15C. 0.33D. None of the above.(c) What is the probability that a randomly chosen American does not have type O blood?A. 0.86B. 0.68C. 0.14D. None of the above

**a) **A probability distribution is called continuous if its distribution function is continuous.

• Answer a: B. continuous.,

**b)**

• Answer b: B. 0.15

**c)**

• Answer c: A. 0.86

Bruno's hourly salary is $8.75. Last week he worked only 18 hours. How much did he earn

It’ll be 157.5 because 8.75 x 18 = 157.5 ^_^

Let g(x) be the indicated transformation .Write the rule for g(x) Linear function defined in the table vertical translation down 2 units I will send you a picture

You have the following data set:

** x 1 0 -3 **

** y 5 4 1 **

Where y is a function of x. In order to translate the previous function 2 unitd downward, you take into account that you subtract 2 units to the given values for y. Then, you have:

**y (5-2) (4-2) (1-2)**

which becomes:

**y 3 2 -1**

Finally, the given table becomes:

** x 1 0 -3 **

** y 2 2 -1 **

3x+3=2(x+7)

What does x equal?

**Answer:** x = 11

**Step-by-step explanation:**

To solve we will **isolate **the **variable**, x.

**Given**:

3x+3=2(x+7)

**Distribute**:

3x+3=2x+14

**Subtract **3 and 2x from both sides of the **equation**:

x = 11

Discount Pricing A wool suit that was originally priced at $700 is on the 30%-off clearance rack. What is the sale price of the suit?

**Answer**:

Sale Price = $490

**Explanation**:

After 30% off, the sale price is 100% - 30% = 70% the original price.

70% of the original price is

[tex]\frac{70\%}{100\%}\times\$700=0.7\times\$700[/tex][tex]=\$490[/tex]which is our answer!

**Hence, the sale price of the wool suit is $490. **

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